Finiteness of J(s|5)

Department of Mathematics, Eckerd College, St. Petersburg, FL 33711

Jianqiang Zhao

This file contains the data to support one of conjectures in my paper Finiteness of p-Divisible Sets of Multiple Harmonic Sums in the special case p=5. Please refer to this paper for unexplained notations.

Conjecture 1. For all s the 5-divisible set J(s|5) is finite.

In each line of the following, we first list s and then the number tau we need in the Criterion Theorem of our main article to compute the 5-divisible set J which is usually {0} if it is not written down.

(1,2): 4,J={0,3}

(1,3): 4

(1,4): 4,J={0,3}

(1,5): 4,J={0,4}

(1,6): 4,J={0,3}

(1,7): 4

(1,8): 4,J={0,3}

(1,9): 4,J={0,4}

(1,10): 4,J={0,3}

(1,11): 4

(1,12): 4,J={0,3}

(1,13): 4,J={0,4}

(1,14): 4,J={0,3}

(1,15): 4

(1,16): 4,J={0,3}

(1,17): 4,J={0,4}

(1,18): 4,J={0,3}

(1,19): 4

(1,20): 4,J={0,3}

(2,2): 3

(2,3): 3

(2,4): 3,J={0,4}

(2,5): 3

(2,6): 3

(2,7): 3

(2,8): 3,J={0,4}

(2,9): 3

(2,10): 3

(2,11): 3

(2,12): 3,J={0,4}

(2,13): 3

(2,14): 3

(2,15): 3

(2,16): 3,J={0,4}

(2,17): 3

(2,18): 3

(2,19): 3

(2,20): 3,J={0,4}

(3,2): 3

(3,3): 3,J={0,4}

(3,4): 3,J={0,4}

(3,5): 3

(3,6): 3

(3,7): 3,J={0,4}

(3,8): 3,J={0,4}

(3,9): 3

(3,10): 3

(3,11): 3,J={0,4}

(3,12): 3,J={0,4}

(3,13): 3

(3,14): 3

(3,15): 3,J={0,4}

(3,16): 3,J={0,4}

(3,17): 3

(3,18): 3

(3,19): 3,J={0,4}

(3,20): 3,J={0,4}

(4,2): 3,J={0,4}

(4,3): 3,J={0,4}

(4,4): 3

(4,5): 3

(4,6): 3,J={0,4}

(4,7): 3,J={0,4}

(4,8): 3

(4,9): 3

(4,10): 3,J={0,4}

(4,11): 3,J={0,4}

(4,12): 3

(4,13): 3

(4,14): 3,J={0,4}

(4,15): 3,J={0,4}

(4,16): 3

(4,17): 3

(4,18): 3,J={0,4}

(4,19): 3,J={0,4}

(4,20): 3

(5,2): 5,J={0,3}

(5,3): 3

(5,4): 3,J={0,3}

(5,5): 3,J={0,4}

(5,6): 3,J={0,3}

(5,7): 3

(5,8): 3,J={0,3}

(5,9): 3,J={0,4}

(5,10): 3,J={0,3}

(5,11): 3

(5,12): 3,J={0,3}

(5,13): 3,J={0,4}

(5,14): 3,J={0,3}

(5,15): 3

(5,16): 3,J={0,3}

(5,17): 3,J={0,4}

(5,18): 3,J={0,3}

(5,19): 3

(5,20): 3,J={0,3}

(6,2): 4

(6,3): 3

(6,4): 3,J={0,4}

(6,5): 3

(6,6): 3

(6,7): 3

(6,8): 3,J={0,4}

(6,9): 3

(6,10): 3

(6,11): 3

(6,12): 3,J={0,4}

(6,13): 3

(6,14): 3

(6,15): 3

(6,16): 3,J={0,4}

(6,17): 3

(6,18): 3

(6,19): 3

(6,20): 3,J={0,4}

(7,2): 5

(7,3): 3,J={0,4}

(7,4): 3,J={0,4}

(7,5): 3

(7,6): 3

(7,7): 3,J={0,4}

(7,8): 3,J={0,4}

(7,9): 3

(7,10): 3

(7,11): 3,J={0,4}

(7,12): 3,J={0,4}

(7,13): 3

(7,14): 3

(7,15): 3,J={0,4}

(7,16): 3,J={0,4}

(7,17): 3

(7,18): 3

(7,19): 3,J={0,4}

(7,20): 3,J={0,4}

(8,2): 5,J={0,4}

(8,3): 3,J={0,4}

(8,4): 3

(8,5): 3

(8,6): 3,J={0,4}

(8,7): 3,J={0,4}

(8,8): 3

(8,9): 3

(8,10): 3,J={0,4}

(8,11): 3,J={0,4}

(8,12): 3

(8,13): 3

(8,14): 3,J={0,4}

(8,15): 3,J={0,4}

(8,16): 3

(8,17): 3

(8,18): 3,J={0,4}

(8,19): 3,J={0,4}

(8,20): 3

(9,2): 7,J={0,3}

(9,3): 5,J={0,5}

(9,4): 4,J={0,3}

(9,5): 3,J={0,4}

(9,6): 3,J={0,3}

(9,7): 3

(9,8): 3,J={0,3}

(9,9): 3,J={0,4}

(9,10): 3,J={0,3}

(9,11): 3

(9,12): 3,J={0,3}

(9,13): 3,J={0,4}

(9,14): 3,J={0,3}

(9,15): 3

(9,16): 3,J={0,3}

(9,17): 3,J={0,4}

(9,18): 3,J={0,3}

(9,19): 3

(9,20): 3,J={0,3}

(10,2): 7

(10,3): 5

(10,4): 4,J={0,4}

(10,5): 3

(10,6): 3

(10,7): 3

(10,8): 3,J={0,4}

(10,9): 3

(10,10): 3

(10,11): 3

(10,12): 3,J={0,4}

(10,13): 3

(10,14): 3

(10,15): 3

(10,16): 3,J={0,4}

(10,17): 3

(10,18): 3

(10,19): 3

(10,20): 3,J={0,4}

(11,2): 7

(11,3): 5,J={0,4}

(11,4): 4,J={0,4}

(11,5): 3

(11,6): 3

(11,7): 3,J={0,4}

(11,8): 3,J={0,4}

(11,9): 3

(11,10): 3

(11,11): 3,J={0,4}

(11,12): 3,J={0,4}

(11,13): 3

(11,14): 3

(11,15): 3,J={0,4}

(11,16): 3,J={0,4}

(11,17): 3

(11,18): 3

(11,19): 3,J={0,4}

(11,20): 3,J={0,4}

(12,2): 7,J={0,4}

(12,3): 5,J={0,4}

(12,4): 4

(12,5): 3

(12,6): 3,J={0,4}

(12,7): 3,J={0,4}

(12,8): 3

(12,9): 3

(12,10): 3,J={0,4}

(12,11): 3,J={0,4}

(12,12): 3

(12,13): 3

(12,14): 3,J={0,4}

(12,15): 3,J={0,4}

(12,16): 3

(12,17): 3

(12,18): 3,J={0,4}

(12,19): 3,J={0,4}

(12,20): 3

(13,2): 8,J={0,3}

(13,3): 6

(13,4): 4,J={0,3}

(13,5): 4,J={0,4}

(13,6): 3,J={0,3}

(13,7): 3

(13,8): 3,J={0,3}

(13,9): 3,J={0,4}

(13,10): 3,J={0,3}

(13,11): 3

(13,12): 3,J={0,3}

(13,13): 3,J={0,4}

(13,14): 3,J={0,3}

(13,15): 3

(13,16): 3,J={0,3}

(13,17): 3,J={0,4}

(13,18): 3,J={0,3}

(13,19): 3

(13,20): 3,J={0,3}

(14,2): 8

(14,3): 6

(14,4): 4,J={0,4}

(14,5): 4

(14,6): 3

(14,7): 3

(14,8): 3,J={0,4}

(14,9): 3

(14,10): 3

(14,11): 3

(14,12): 3,J={0,4}

(14,13): 3

(14,14): 3

(14,15): 3

(14,16): 3,J={0,4}

(14,17): 3

(14,18): 3

(14,19): 3

(14,20): 3,J={0,4}

(15,2): 10

(15,3): 6,J={0,4}

(15,4): 5,J={0,4}

(15,5): 4

(15,6): 3

(15,7): 3,J={0,4}

(15,8): 3,J={0,4}

(15,9): 3

(15,10): 3

(15,11): 3,J={0,4}

(15,12): 3,J={0,4}

(15,13): 3

(15,14): 3

(15,15): 3,J={0,4}

(15,16): 3,J={0,4}

(15,17): 3

(15,18): 3

(15,19): 3,J={0,4}

(15,20): 3,J={0,4}

(16,2): 9,J={0,4}

(16,3): 6,J={0,4}

(16,4): 5

(16,5): 4

(16,6): 3,J={0,4}

(16,7): 3,J={0,4}

(16,8): 3

(16,9): 3

(16,10): 3,J={0,4}

(16,11): 3,J={0,4}

(16,12): 3

(16,13): 3

(16,14): 3,J={0,4}

(16,15): 3,J={0,4}

(16,16): 3

(16,17): 3

(16,18): 3,J={0,4}

(16,19): 3,J={0,4}

(16,20): 3

(17,2): 11,J={0,3,5}

(17,3): 7

(17,4): 5,J={0,3}

(17,5): 4,J={0,4}

(17,6): 4,J={0,3}

(17,7): 3

(17,8): 3,J={0,3}

(17,9): 3,J={0,4}

(17,10): 3,J={0,3}

(17,11): 3

(17,12): 3,J={0,3}

(17,13): 3,J={0,4}

(17,14): 3,J={0,3}

(17,15): 3

(17,16): 3,J={0,3}

(17,17): 3,J={0,4}

(17,18): 3,J={0,3}

(17,19): 3

(17,20): 3,J={0,3}

(18,2): 11

(18,3): 7

(18,4): 5,J={0,4}

(18,5): 4

(18,6): 4

(18,7): 3

(18,8): 3,J={0,4}

(18,9): 3

(18,10): 3

(18,11): 3

(18,12): 3,J={0,4}

(18,13): 3

(18,14): 3

(18,15): 3

(18,16): 3,J={0,4}

(18,17): 3

(18,18): 3

(18,19): 3

(18,20): 3,J={0,4}

(19,2): 11

(19,3): 7,J={0,4}

(19,4): 6,J={0,4}

(19,5): 5

(19,6): 4

(19,7): 3,J={0,4}

(19,8): 3,J={0,4}

(19,9): 3

(19,10): 3

(19,11): 3,J={0,4}

(19,12): 3,J={0,4}

(19,13): 3

(19,14): 3

(19,15): 3,J={0,4}

(19,16): 3,J={0,4}

(19,17): 3

(19,18): 3

(19,19): 3,J={0,4}

(19,20): 3,J={0,4}

(20,2): 11,J={0,4}

(20,3): 7,J={0,4}

(20,4): 6

(20,5): 5

(20,6): 4,J={0,4}

(20,7): 3,J={0,4}

(20,8): 3

(20,9): 3

(20,10): 3,J={0,4}

(20,11): 3,J={0,4}

(20,12): 3

(20,13): 3

(20,14): 3,J={0,4}

(20,15): 3,J={0,4}

(20,16): 3

(20,17): 3

(20,18): 3,J={0,4}

(20,19): 3,J={0,4}

(20,20): 3

(1,1,2): 4

(1,1,3): 4

(1,1,4): 4

(1,1,5): 4,J={0,4}

(1,1,6): 5

(1,1,7): 4

(1,1,8): 4

(1,1,9): 4,J={0,4}

(1,1,10): 5

(1,2,2): 9

(1,2,3): 4

(1,2,4): 8

(1,2,5): 4

(1,2,6): 4

(1,2,7): 4

(1,2,8): 5

(1,2,9): 4

(1,2,10): 4

(1,3,2): 6

(1,3,3): 5

(1,3,4): 5

(1,3,5): 5,J={0,4}

(1,3,6): 5

(1,3,7): 5

(1,3,8): 5

(1,3,9): 5,J={0,4}

(1,3,10): 5

(1,4,2): 6

(1,4,3): 6

(1,4,4): 6

(1,4,5): 6

(1,4,6): 6

(1,4,7): 6

(1,4,8): 6

(1,4,9): 6

(1,4,10): 6

(1,5,2): 9

(1,5,3): 8

(1,5,4): 9

(1,5,5): 8,J={0,4}

(1,5,6): 8

(1,5,7): 8

(1,5,8): 8

(1,5,9): 8,J={0,4}

(1,5,10): 8

(1,6,2): 8

(1,6,3): 8

(1,6,4): 9

(1,6,5): 8

(1,6,6): 8

(1,6,7): 8

(1,6,8): 8

(1,6,9): 8

(1,6,10): 8

(1,7,2): 10

(1,7,3): 9

(1,7,4): 9

(1,7,5): 10,J={0,4}

(1,7,6): 9

(1,7,7): 9

(1,7,8): 9

(1,7,9): 9,J={0,4}

(1,7,10): 9

(1,8,2): 10

(1,8,3): 11

(1,8,4): 10

(1,8,5): 10

(1,8,6): 10

(1,8,7): 10

(1,8,8): 10

(1,8,9): 10

(1,8,10): 10

(1,9,2): 13

(1,9,3): 13

(1,9,4): 13

(1,9,5): 13

(1,9,6): 13

(1,9,7): 13

(1,9,8): 13

(1,9,9): 13

(1,9,10): 13

(1,10,2): 13

(1,10,3): 13

(1,10,4): 13

(1,10,5): 13

(1,10,6): 13

(1,10,7): 13

(1,10,8): 13

(1,10,9): 13

(1,10,10): 13

(2,1,2): 5,J={0,4}

(2,1,3): 5

(2,1,4): 6

(2,1,5): 4

(2,1,6): 4,J={0,4}

(2,1,7): 4

(2,1,8): 5

(2,1,9): 4

(2,1,10): 4,J={0,4}

(2,2,2): 4,J={0,4}

(2,2,3): 3

(2,2,4): 3

(2,2,5): 3

(2,2,6): 3,J={0,4}

(2,2,7): 3

(2,2,8): 3

(2,2,9): 3

(2,2,10): 3,J={0,4}

(2,3,2): 4,J={0,4}

(2,3,3): 3

(2,3,4): 3

(2,3,5): 3

(2,3,6): 3,J={0,4}

(2,3,7): 3

(2,3,8): 3

(2,3,9): 3

(2,3,10): 3,J={0,4}

(2,4,2): 6,J={0,4}

(2,4,3): 4

(2,4,4): 5

(2,4,5): 4

(2,4,6): 4,J={0,4}

(2,4,7): 4

(2,4,8): 4

(2,4,9): 4

(2,4,10): 4,J={0,4}

(2,5,2): 6,J={0,4}

(2,5,3): 4

(2,5,4): 5

(2,5,5): 4

(2,5,6): 4,J={0,4}

(2,5,7): 4

(2,5,8): 4

(2,5,9): 4

(2,5,10): 4,J={0,4}

(2,6,2): 5,J={0,4}

(2,6,3): 5

(2,6,4): 5

(2,6,5): 5

(2,6,6): 5,J={0,4}

(2,6,7): 5

(2,6,8): 5

(2,6,9): 5

(2,6,10): 5,J={0,4}

(2,7,2): 5,J={0,4}

(2,7,3): 7

(2,7,4): 5

(2,7,5): 5

(2,7,6): 5,J={0,4}

(2,7,7): 5

(2,7,8): 5

(2,7,9): 5

(2,7,10): 5,J={0,4}

(2,8,2): 6,J={0,4}

(2,8,3): 6

(2,8,4): 7

(2,8,5): 7

(2,8,6): 6,J={0,4}

(2,8,7): 6

(2,8,8): 7

(2,8,9): 6

(2,8,10): 6,J={0,4}

(2,9,2): 7,J={0,4}

(2,9,3): 6

(2,9,4): 7

(2,9,5): 6

(2,9,6): 6,J={0,4}

(2,9,7): 6

(2,9,8): 7

(2,9,9): 6

(2,9,10): 6,J={0,4}

(2,10,2): 7,J={0,4}

(2,10,3): 7

(2,10,4): 7

(2,10,5): 7

(2,10,6): 7,J={0,4}

(2,10,7): 7

(2,10,8): 7

(2,10,9): 7

(2,10,10): 7,J={0,4}

(3,1,2): 5

(3,1,3): 6,J={0,4}

(3,1,4): 5

(3,1,5): 5

(3,1,6): 5

(3,1,7): 5,J={0,4}

(3,1,8): 5

(3,1,9): 5

(3,1,10): 5

(3,2,2): 3

(3,2,3): 5

(3,2,4): 3,J={0,4}

(3,2,5): 3

(3,2,6): 3

(3,2,7): 3

(3,2,8): 3,J={0,4}

(3,2,9): 3

(3,2,10): 3

(3,3,2): 4

(3,3,3): 3,J={0,4}

(3,3,4): 3

(3,3,5): 3

(3,3,6): 3

(3,3,7): 3,J={0,4}

(3,3,8): 3

(3,3,9): 3

(3,3,10): 3

(3,4,2): 5

(3,4,3): 4

(3,4,4): 4,J={0,4}

(3,4,5): 5

(3,4,6): 4

(3,4,7): 4

(3,4,8): 4,J={0,4}

(3,4,9): 4

(3,4,10): 4

(3,5,2): 5

(3,5,3): 3,J={0,4}

(3,5,4): 4

(3,5,5): 3

(3,5,6): 3

(3,5,7): 3,J={0,4}

(3,5,8): 3

(3,5,9): 3

(3,5,10): 3

(3,6,2): 5

(3,6,3): 4

(3,6,4): 4,J={0,4}

(3,6,5): 4

(3,6,6): 4

(3,6,7): 4

(3,6,8): 4,J={0,4}

(3,6,9): 4

(3,6,10): 4

(3,7,2): 7

(3,7,3): 5,J={0,4}

(3,7,4): 5

(3,7,5): 5

(3,7,6): 5

(3,7,7): 5,J={0,4}

(3,7,8): 5

(3,7,9): 5

(3,7,10): 5

(3,8,2): 7

(3,8,3): 5

(3,8,4): 5,J={0,4}

(3,8,5): 5

(3,8,6): 5

(3,8,7): 5

(3,8,8): 5,J={0,4}

(3,8,9): 5

(3,8,10): 5

(3,9,2): 7

(3,9,3): 5,J={0,4}

(3,9,4): 5

(3,9,5): 5

(3,9,6): 5

(3,9,7): 6,J={0,4}

(3,9,8): 5

(3,9,9): 5

(3,9,10): 5

(3,10,2): 7

(3,10,3): 5

(3,10,4): 5,J={0,4}

(3,10,5): 5

(3,10,6): 5

(3,10,7): 5

(3,10,8): 5,J={0,4}

(3,10,9): 5

(3,10,10): 5

(4,1,2): 7

(4,1,3): 6

(4,1,4): 8,J={0,4}

(4,1,5): 6

(4,1,6): 6

(4,1,7): 6

(4,1,8): 6,J={0,4}

(4,1,9): 6

(4,1,10): 6

(4,2,2): 5

(4,2,3): 5,J={0,4}

(4,2,4): 5

(4,2,5): 5

(4,2,6): 5

(4,2,7): 5,J={0,4}

(4,2,8): 5

(4,2,9): 5

(4,2,10): 5

(4,3,2): 6,J={0,5}

(4,3,3): 4

(4,3,4): 4,J={0,4}

(4,3,5): 4

(4,3,6): 4

(4,3,7): 4

(4,3,8): 4,J={0,4}

(4,3,9): 4

(4,3,10): 4

(4,4,2): 5

(4,4,3): 3,J={0,4}

(4,4,4): 3

(4,4,5): 3

(4,4,6): 3

(4,4,7): 3,J={0,4}

(4,4,8): 3

(4,4,9): 3

(4,4,10): 3

(4,5,2): 7

(4,5,3): 4

(4,5,4): 3,J={0,4}

(4,5,5): 3

(4,5,6): 3

(4,5,7): 3

(4,5,8): 3,J={0,4}

(4,5,9): 3

(4,5,10): 3

(4,6,2): 6

(4,6,3): 4,J={0,4}

(4,6,4): 3

(4,6,5): 3

(4,6,6): 4

(4,6,7): 3,J={0,4}

(4,6,8): 3

(4,6,9): 3

(4,6,10): 3

(4,7,2): 8

(4,7,3): 5

(4,7,4): 4,J={0,4}

(4,7,5): 4

(4,7,6): 4

(4,7,7): 4

(4,7,8): 4,J={0,4}

(4,7,9): 4

(4,7,10): 4

(4,8,2): 7

(4,8,3): 5,J={0,4}

(4,8,4): 4

(4,8,5): 4

(4,8,6): 4

(4,8,7): 4,J={0,4}

(4,8,8): 4

(4,8,9): 4

(4,8,10): 4

(4,9,2): 9

(4,9,3): 5

(4,9,4): 4,J={0,4}

(4,9,5): 4

(4,9,6): 4

(4,9,7): 4

(4,9,8): 4,J={0,4}

(4,9,9): 4

(4,9,10): 4

(4,10,2): 9

(4,10,3): 6,J={0,4}

(4,10,4): 4

(4,10,5): 4

(4,10,6): 4

(4,10,7): 4,J={0,4}

(4,10,8): 4

(4,10,9): 4

(4,10,10): 4

(5,1,2): 8

(5,1,3): 10

(5,1,4): 8

(5,1,5): 8,J={0,4}

(5,1,6): 10

(5,1,7): 8

(5,1,8): 8

(5,1,9): 8,J={0,4}

(5,1,10): 8

(5,2,2): 5

(5,2,3): 4

(5,2,4): 4

(5,2,5): 5

(5,2,6): 4

(5,2,7): 4

(5,2,8): 4

(5,2,9): 4

(5,2,10): 4

(5,3,2): 5

(5,3,3): 3

(5,3,4): 3

(5,3,5): 3,J={0,4}

(5,3,6): 3

(5,3,7): 3

(5,3,8): 3

(5,3,9): 3,J={0,4}

(5,3,10): 3

(5,4,2): 7

(5,4,3): 4

(5,4,4): 3

(5,4,5): 4

(5,4,6): 3

(5,4,7): 3

(5,4,8): 3

(5,4,9): 3

(5,4,10): 3

(5,5,2): 7

(5,5,3): 5

(5,5,4): 4

(5,5,5): 3,J={0,4}

(5,5,6): 3

(5,5,7): 3

(5,5,8): 3

(5,5,9): 3,J={0,4}

(5,5,10): 3

(5,6,2): 6

(5,6,3): 5

(5,6,4): 3

(5,6,5): 3

(5,6,6): 3

(5,6,7): 3

(5,6,8): 3

(5,6,9): 3

(5,6,10): 3

(5,7,2): 7

(5,7,3): 5

(5,7,4): 4

(5,7,5): 3,J={0,4}

(5,7,6): 3

(5,7,7): 3

(5,7,8): 3

(5,7,9): 3,J={0,4}

(5,7,10): 3

(5,8,2): 7

(5,8,3): 5

(5,8,4): 4

(5,8,5): 4

(5,8,6): 3

(5,8,7): 3

(5,8,8): 3

(5,8,9): 3

(5,8,10): 3

(5,9,2): 9

(5,9,3): 6

(5,9,4): 4

(5,9,5): 4,J={0,4}

(5,9,6): 4

(5,9,7): 4

(5,9,8): 4

(5,9,9): 4,J={0,4}

(5,9,10): 4

(5,10,2): 8

(5,10,3): 6

(5,10,4): 4

(5,10,5): 4

(5,10,6): 4

(5,10,7): 4

(5,10,8): 4

(5,10,9): 4

(5,10,10): 4

(6,1,2): 8,J={0,4}

(6,1,3): 9

(6,1,4): 8

(6,1,5): 8

(6,1,6): 9,J={0,4}

(6,1,7): 8

(6,1,8): 8

(6,1,9): 8

(6,1,10): 8,J={0,4}

(6,2,2): 5,J={0,4}

(6,2,3): 5

(6,2,4): 5

(6,2,5): 5

(6,2,6): 5,J={0,4}

(6,2,7): 5

(6,2,8): 5

(6,2,9): 5

(6,2,10): 5,J={0,4}

(6,3,2): 6,J={0,4}

(6,3,3): 4

(6,3,4): 4

(6,3,5): 4

(6,3,6): 4,J={0,4}

(6,3,7): 4

(6,3,8): 4

(6,3,9): 4

(6,3,10): 4,J={0,4}

(6,4,2): 6,J={0,4}

(6,4,3): 4

(6,4,4): 3

(6,4,5): 3

(6,4,6): 3,J={0,4}

(6,4,7): 3

(6,4,8): 3

(6,4,9): 3

(6,4,10): 3,J={0,4}

(6,5,2): 6,J={0,4}

(6,5,3): 4

(6,5,4): 3

(6,5,5): 3

(6,5,6): 3,J={0,4}

(6,5,7): 3

(6,5,8): 3

(6,5,9): 3

(6,5,10): 3,J={0,4}

(6,6,2): 7,J={0,4}

(6,6,3): 5

(6,6,4): 4

(6,6,5): 3

(6,6,6): 3,J={0,4}

(6,6,7): 3

(6,6,8): 3

(6,6,9): 3

(6,6,10): 3,J={0,4}

(6,7,2): 8,J={0,4}

(6,7,3): 6

(6,7,4): 4

(6,7,5): 3

(6,7,6): 3,J={0,4}

(6,7,7): 3

(6,7,8): 3

(6,7,9): 3

(6,7,10): 3,J={0,4}

(6,8,2): 8,J={0,4}

(6,8,3): 6

(6,8,4): 5

(6,8,5): 4

(6,8,6): 3,J={0,4}

(6,8,7): 3

(6,8,8): 3

(6,8,9): 3

(6,8,10): 3,J={0,4}

(6,9,2): 8,J={0,4}

(6,9,3): 6

(6,9,4): 5

(6,9,5): 4

(6,9,6): 3,J={0,4}

(6,9,7): 3

(6,9,8): 3

(6,9,9): 3

(6,9,10): 3,J={0,4}

(6,10,2): 9,J={0,4}

(6,10,3): 6

(6,10,4): 5

(6,10,5): 4

(6,10,6): 3,J={0,4}

(6,10,7): 3

(6,10,8): 3

(6,10,9): 4

(6,10,10): 3,J={0,4}

(7,1,2): 9

(7,1,3): 10,J={0,4}

(7,1,4): 9

(7,1,5): 9

(7,1,6): 10

(7,1,7): 10,J={0,4}

(7,1,8): 9

(7,1,9): 9

(7,1,10): 9

(7,2,2): 5

(7,2,3): 5

(7,2,4): 5,J={0,4}

(7,2,5): 5

(7,2,6): 5

(7,2,7): 6

(7,2,8): 5,J={0,4}

(7,2,9): 5

(7,2,10): 5

(7,3,2): 7,J={0,5}

(7,3,3): 5,J={0,4}

(7,3,4): 5

(7,3,5): 5

(7,3,6): 5

(7,3,7): 5,J={0,4}

(7,3,8): 5

(7,3,9): 5

(7,3,10): 5

(7,4,2): 7

(7,4,3): 5

(7,4,4): 4,J={0,4}

(7,4,5): 5

(7,4,6): 4

(7,4,7): 4

(7,4,8): 4,J={0,4}

(7,4,9): 4

(7,4,10): 4

(7,5,2): 7

(7,5,3): 5,J={0,4}

(7,5,4): 4

(7,5,5): 3

(7,5,6): 3

(7,5,7): 3,J={0,4}

(7,5,8): 3

(7,5,9): 3

(7,5,10): 3

(7,6,2): 7

(7,6,3): 5

(7,6,4): 4,J={0,4}

(7,6,5): 3

(7,6,6): 3

(7,6,7): 3

(7,6,8): 3,J={0,4}

(7,6,9): 3

(7,6,10): 3

(7,7,2): 9

(7,7,3): 6,J={0,4}

(7,7,4): 4

(7,7,5): 4

(7,7,6): 3

(7,7,7): 3,J={0,4}

(7,7,8): 3

(7,7,9): 3

(7,7,10): 3

(7,8,2): 9

(7,8,3): 6

(7,8,4): 5,J={0,4}

(7,8,5): 4

(7,8,6): 3

(7,8,7): 3

(7,8,8): 3,J={0,4}

(7,8,9): 3

(7,8,10): 3

(7,9,2): 9

(7,9,3): 6,J={0,4}

(7,9,4): 5

(7,9,5): 4

(7,9,6): 3

(7,9,7): 3,J={0,4}

(7,9,8): 3

(7,9,9): 3

(7,9,10): 3

(7,10,2): 9

(7,10,3): 7

(7,10,4): 5,J={0,4}

(7,10,5): 4

(7,10,6): 3

(7,10,7): 3

(7,10,8): 3,J={0,4}

(7,10,9): 3

(7,10,10): 3

(8,1,2): 13

(8,1,3): 10

(8,1,4): 10,J={0,4}

(8,1,5): 10

(8,1,6): 10

(8,1,7): 10

(8,1,8): 13,J={0,4}

(8,1,9): 10

(8,1,10): 10

(8,2,2): 6

(8,2,3): 6,J={0,4}

(8,2,4): 6

(8,2,5): 6

(8,2,6): 6

(8,2,7): 6,J={0,4}

(8,2,8): 6

(8,2,9): 6

(8,2,10): 6

(8,3,2): 7

(8,3,3): 5

(8,3,4): 5,J={0,4}

(8,3,5): 5

(8,3,6): 6

(8,3,7): 5

(8,3,8): 5,J={0,4}

(8,3,9): 5

(8,3,10): 5

(8,4,2): 8

(8,4,3): 5,J={0,4}

(8,4,4): 4

(8,4,5): 4

(8,4,6): 4

(8,4,7): 4,J={0,4}

(8,4,8): 4

(8,4,9): 4

(8,4,10): 4

(8,5,2): 8

(8,5,3): 5

(8,5,4): 4,J={0,4}

(8,5,5): 3

(8,5,6): 3

(8,5,7): 3

(8,5,8): 4,J={0,4}

(8,5,9): 3

(8,5,10): 3

(8,6,2): 8

(8,6,3): 6,J={0,4}

(8,6,4): 4

(8,6,5): 4

(8,6,6): 3

(8,6,7): 3,J={0,4}

(8,6,8): 3

(8,6,9): 3

(8,6,10): 3

(8,7,2): 9

(8,7,3): 6

(8,7,4): 5,J={0,4}

(8,7,5): 4

(8,7,6): 3

(8,7,7): 3

(8,7,8): 3,J={0,4}

(8,7,9): 3

(8,7,10): 3

(8,8,2): 9

(8,8,3): 6,J={0,4}

(8,8,4): 5

(8,8,5): 4

(8,8,6): 3

(8,8,7): 3,J={0,4}

(8,8,8): 3

(8,8,9): 3

(8,8,10): 3

(8,9,2): 10

(8,9,3): 6

(8,9,4): 5,J={0,4}

(8,9,5): 4

(8,9,6): 3

(8,9,7): 3

(8,9,8): 3,J={0,4}

(8,9,9): 3

(8,9,10): 3

(8,10,2): 10

(8,10,3): 7,J={0,4}

(8,10,4): 5

(8,10,5): 4

(8,10,6): 4

(8,10,7): 3,J={0,4}

(8,10,8): 3

(8,10,9): 3

(8,10,10): 3

(9,1,2): 14

(9,1,3): 13

(9,1,4): 14

(9,1,5): 12,J={0,4}

(9,1,6): 12

(9,1,7): 12

(9,1,8): 13

(9,1,9): 12,J={0,4}

(9,1,10): 15 (It takes 36 days to find this on my PC with 3.06GHZ CPU and 512 KB memory.)

(9,2,2): 7

(9,2,3): 6

(9,2,4): 6

(9,2,5): 6

(9,2,6): 7

(9,2,7): 6

(9,2,8): 6

(9,2,9): 7

(9,2,10): 6

(9,3,2): 7

(9,3,3): 5

(9,3,4): 5

(9,3,5): 5,J={0,4}

(9,3,6): 5

(9,3,7): 5

(9,3,8): 5

(9,3,9): 5,J={0,4}

(9,3,10): 5

(9,4,2): 7

(9,4,3): 5

(9,4,4): 4

(9,4,5): 4

(9,4,6): 4

(9,4,7): 4

(9,4,8): 4

(9,4,9): 4

(9,4,10): 4

(9,5,2): 9

(9,5,3): 6

(9,5,4): 4

(9,5,5): 4,J={0,4}

(9,5,6): 4

(9,5,7): 4

(9,5,8): 4

(9,5,9): 4,J={0,4}

(9,5,10): 4

(9,6,2): 8

(9,6,3): 6

(9,6,4): 4

(9,6,5): 4

(9,6,6): 3

(9,6,7): 3

(9,6,8): 3

(9,6,9): 3

(9,6,10): 3

(9,7,2): 9

(9,7,3): 6

(9,7,4): 5

(9,7,5): 4,J={0,4}

(9,7,6): 3

(9,7,7): 3

(9,7,8): 3

(9,7,9): 3,J={0,4}

(9,7,10): 3

(9,8,2): 9

(9,8,3): 6

(9,8,4): 5

(9,8,5): 4

(9,8,6): 3

(9,8,7): 3

(9,8,8): 3

(9,8,9): 3

(9,8,10): 3

(9,9,2): 12

(9,9,3): 8

(9,9,4): 5

(9,9,5): 4,J={0,4}

(9,9,6): 4

(9,9,7): 3

(9,9,8): 3

(9,9,9): 3,J={0,4}

(9,9,10): 3

(9,10,2): 10

(9,10,3): 7

(9,10,4): 5

(9,10,5): 4

(9,10,6): 4

(9,10,7): 3

(9,10,8): 3

(9,10,9): 3

(9,10,10): 3

(10,1,2): 13

(10,1,3): 13

(10,1,4): 13

(10,1,5): 12

(10,1,6): 12,J={0,4}

(10,1,7): 12

(10,1,8): 12

(10,1,9): 12

(10,1,10): 13,J={0,4}

(10,2,2): 7,J={0,4}

(10,2,3): 7

(10,2,4): 7

(10,2,5): 7

(10,2,6): 7,J={0,4}

(10,2,7): 7

(10,2,8): 7

(10,2,9): 7

(10,2,10): 7,J={0,4}

(10,3,2): 7,J={0,4}

(10,3,3): 5

(10,3,4): 5

(10,3,5): 5

(10,3,6): 5,J={0,4}

(10,3,7): 5

(10,3,8): 5

(10,3,9): 5

(10,3,10): 6,J={0,4}

(10,4,2): 8,J={0,4}

(10,4,3): 6

(10,4,4): 4

(10,4,5): 4

(10,4,6): 4,J={0,4}

(10,4,7): 4

(10,4,8): 4

(10,4,9): 4

(10,4,10): 4,J={0,4}

(10,5,2): 9,J={0,4}

(10,5,3): 6

(10,5,4): 4

(10,5,5): 4

(10,5,6): 4,J={0,4}

(10,5,7): 4

(10,5,8): 4

(10,5,9): 4

(10,5,10): 4,J={0,4}

(10,6,2): 9,J={0,4}

(10,6,3): 6

(10,6,4): 5

(10,6,5): 4

(10,6,6): 3,J={0,4}

(10,6,7): 3

(10,6,8): 3

(10,6,9): 3

(10,6,10): 3,J={0,4}

(10,7,2): 9,J={0,4}

(10,7,3): 6

(10,7,4): 5

(10,7,5): 4

(10,7,6): 3,J={0,4}

(10,7,7): 3

(10,7,8): 3

(10,7,9): 3

(10,7,10): 3,J={0,4}

(10,8,2): 10,J={0,4}

(10,8,3): 7

(10,8,4): 5

(10,8,5): 4

(10,8,6): 4,J={0,4}

(10,8,7): 3

(10,8,8): 3

(10,8,9): 3

(10,8,10): 3,J={0,4}

(10,9,2): 12,J={0,4}

(10,9,3): 7

(10,9,4): 5

(10,9,5): 4

(10,9,6): 4,J={0,4}

(10,9,7): 3

(10,9,8): 3

(10,9,9): 3

(10,9,10): 3,J={0,4}

(10,10,2): 11,J={0,4}

(10,10,3): 7

(10,10,4): 6

(10,10,5): 5

(10,10,6): 4,J={0,4}

(10,10,7): 3

(10,10,8): 3

(10,10,9): 3

(10,10,10): 3,J={0,4}

(1,1,1,2): 6

(1,1,1,3): 5

(1,1,1,4): 5

(1,1,1,5): 5

(1,1,1,6): 5

(1,1,1,7): 5

(1,1,1,8): 5

(1,1,1,9): 5

(1,1,1,10): 5

(1,1,2,2): 5

(1,1,2,3): 6

(1,1,2,4): 5

(1,1,2,5): 5

(1,1,2,6): 5

(1,1,2,7): 5

(1,1,2,8): 5

(1,1,2,9): 5

(1,1,2,10): 5

(1,1,3,2): 11

(1,1,3,3): 6

(1,1,3,4): 6

(1,1,3,5): 6

(1,1,3,6): 6

(1,1,3,7): 6

(1,1,3,8): 6

(1,1,3,9): 6

(1,1,3,10): 6

(1,1,4,2): 7

(1,1,4,3): 7

(1,1,4,4): 7

(1,1,4,5): 7

(1,1,4,6): 7

(1,1,4,7): 7

(1,1,4,8): 7

(1,1,4,9): 7

(1,1,4,10): 7

(1,1,5,3): 9

(1,1,5,4): 9

(1,1,5,5): 10

(1,1,5,6): 9

(1,1,5,7): 9

(1,1,5,8): 9

(1,1,5,9): 9

(1,1,5,10): 9

(1,1,6,2): 10

(1,1,6,3): 9

(1,1,6,4): 9

(1,1,6,5): 10

(1,1,6,6): 9

(1,1,6,7): 9

(1,1,6,8): 9

(1,1,6,9): 9

(1,1,6,10): 9

(1,1,7,3): 10

(1,1,7,4): 10

(1,1,7,5): 10

(1,1,7,7): 10

(1,1,7,8): 10

(1,1,7,9): 10

(1,1,7,10): 10

(1,2,1,2): 8

(1,2,1,3): 7

(1,2,1,4): 5

(1,2,2,2): 8

(1,2,2,3): 6

(1,2,2,4): 6

(1,2,3,2): 9

(1,2,3,3): 8

(1,2,3,4): 7

(1,2,4,2): 9

(1,2,4,3): 8

(1,2,4,4): 10

(1,3,1,2): 8

(1,3,1,3): 9

(1,3,1,4): 8

(1,3,2,2): 8

(1,3,2,3): 7

(1,3,2,4): 7

(1,3,3,2): 8

(1,3,3,3): 10

(1,3,3,4): 8

(1,3,4,2): 9

(1,3,4,3): 9

(1,3,4,4): 11

(1,4,1,2): 8

(1,4,1,3): 7

(1,4,1,4): 7

(1,4,2,2): 9

(1,4,2,3): 8

(1,4,2,4): 8

(1,4,3,2): 9

(1,4,3,3): 9

(1,4,3,4): 9

(1,4,4,2): 11

(1,4,4,3): 10

(1,4,4,4): 11

(2,1,1,2): 6

(2,1,1,3): 5

(2,1,1,4): 5

(2,1,2,2): 8

(2,1,2,3): 8

(2,1,2,4): 7

(2,1,3,2): 7

(2,1,3,3): 8

(2,1,3,4): 7

(2,1,4,2): 9

(2,1,4,3): 8

(2,1,4,4): 9

(2,2,1,2): 6

(2,2,1,3): 6

(2,2,1,4): 6

(2,2,2,2): 4

(2,2,2,3): 5

(2,2,2,4): 4

(2,2,3,2): 7

(2,2,3,3): 4

(2,2,3,4): 4

(2,2,4,2): 5

(2,2,4,3): 5

(2,2,4,4): 5

(2,3,1,2): 10

(2,3,1,3): 7

(2,3,1,4): 7

(2,3,2,2): 5

(2,3,2,3): 6

(2,3,2,4): 5

(2,3,3,2): 5

(2,3,3,3): 5

(2,3,3,4): 5

(2,3,4,2): 5

(2,3,4,3): 6

(2,3,4,4): 6

(2,4,1,2): 8

(2,4,1,3): 8

(2,4,1,4): 8

(2,4,2,2): 5

(2,4,2,3): 5

(2,4,2,4): 5

(2,4,3,2): 5

(2,4,3,3): 6

(2,4,3,4): 5

(2,4,4,2): 6

(2,4,4,3): 6

(2,4,4,4): 6

(3,1,1,2): 6

(3,1,1,3): 8

(3,1,1,4): 6

(3,1,2,2): 9

(3,1,2,3): 7

(3,1,2,4): 7

(3,1,3,2): 9

(3,1,3,3): 9

(3,1,3,4): 9

(3,1,4,2): 10

(3,1,4,3): 9

(3,1,4,4): 10

(3,2,1,2): 7

(3,2,1,3): 7

(3,2,1,4): 7

(3,2,2,2): 4

(3,2,2,3): 5

(3,2,2,4): 4

(3,2,3,2): 5

(3,2,3,3): 5

(3,2,3,4): 5

(3,2,4,2): 9

(3,2,4,3): 6

(3,2,4,4): 6

(3,3,1,2): 8

(3,3,1,3): 8

(3,3,1,4): 8

(3,3,2,2): 5

(3,3,2,3): 5

(3,3,2,4): 5

(3,3,3,2): 6

(3,3,3,3): 4

(3,3,3,4): 5

(3,3,4,2): 6

(3,3,4,3): 4

(3,3,4,4): 4

(3,4,1,2): 9

(3,4,1,3): 9

(3,4,1,4): 9

(3,4,2,2): 5

(3,4,2,3): 6

(3,4,2,4): 5

(3,4,3,2): 6

(3,4,3,3): 4

(3,4,3,4): 4

(3,4,4,2): 7

(3,4,4,3): 5

(3,4,4,4): 5

(4,1,1,2): 8

(4,1,1,3): 7

(4,1,1,4): 7

(4,1,2,2): 10

(4,1,2,3): 8

(4,1,2,4): 8

(4,1,3,2): 9

(4,1,3,3): 9

(4,1,3,4): 9

(4,1,4,2): 11

(4,1,4,3): 11

(4,1,4,4): 11

(4,2,1,2): 9

(4,2,1,3): 8

(4,2,1,4): 8

(4,2,2,2): 5

(4,2,2,3): 5

(4,2,2,4): 5

(4,2,3,2): 6

(4,2,3,3): 6

(4,2,3,4): 6

(4,2,4,2): 6

(4,2,4,3): 6

(4,2,4,4): 6

(4,3,1,2): 9

(4,3,1,3): 9

(4,3,1,4): 9

(4,3,2,2): 5

(4,3,2,3): 5

(4,3,2,4): 6

(4,3,3,2): 6

(4,3,3,3): 4

(4,3,3,4): 4

(4,3,4,2): 8

(4,3,4,3): 5

(4,3,4,4): 5

(4,4,1,2): 11

(4,4,1,3): 10

(4,4,1,4): 10

(4,4,2,2): 6

(4,4,2,3): 7

(4,4,2,4): 6

(4,4,3,2): 7

(4,4,3,3): 5

(4,4,3,4): 5

(4,4,4,2): 7

(4,4,4,3): 5

(4,4,4,4): 4