A246134 Binomial(2n, n) - 2 mod n^4.

0, 4, 18, 68, 250, 922, 1029, 580, 2691, 4754, 2662, 8474, 4394, 10294, 2518, 49732, 29478, 65074, 123462, 128818, 6535, 93174, 36501, 12058, 187750, 162582, 297936, 273782, 536558, 741422, 59582, 16964, 118477, 540434, 132305, 136130, 1114366, 1138598, 2214594, 2381618, 1860867, 2795686, 1828661, 1775622, 2683618, 1435710, 1557345, 3882778

Offset: 1

Author

Stanislav Sykora, Aug 16 2014

Keywords

• nonn

Comments

For e > 3, unlike the cases e=1,2,3, the numbers binomial(2n, n) - 2 mod n^e are not necessarily 0 for any n>1, be it prime or composite (see A246130 for introductory comments). Testing up to n=278000, the only number n>1 for which a(n)=0 is the first Wolstenholme prime 16843 (A088164), but no composite.

Examples

			a(7) = (binomial(14,7)-2) mod 7^4 = (3432-2) mod 2401 = 1029.
		

Links

• Stanislav Sykora, Table of n, a(n) for n = 1..10000
• R. J. McIntosh, On the converse of Wolstenholme's theorem, Acta Arithmetica 71 (4): 381-389, (1995)
• Wikipedia, Wolstenholme's theorem

Crossrefs

Cf. A000984, A088164, A246130 (e=1), A246132 (e=2), A246133 (e=3).

Programs

PARI

a(n) = (binomial(2*n,n)-2)%n^4