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A246134
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Binomial(2n, n) - 2 mod n^4.
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6
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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
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OFFSET
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1,2
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COMMENTS
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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.
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LINKS
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EXAMPLE
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a(7) = (binomial(14,7)-2) mod 7^4 = (3432-2) mod 2401 = 1029.
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PROG
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(PARI) a(n) = (binomial(2*n, n)-2)%n^4
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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