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A133906
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Least number m such that binomial(n+m, m) mod m = 1.
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5
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2, 3, 5, 2, 2, 7, 9, 2, 2, 3, 3, 2, 2, 17, 17, 2, 2, 3, 3, 2, 2, 23, 25, 2, 2, 4, 3, 2, 2, 31, 37, 2, 2, 8, 8, 2, 2, 3, 41, 2, 2, 4, 4, 2, 2, 3, 3, 2, 2, 5, 5, 2, 2, 3, 3, 2, 2, 4, 4, 2, 2, 67, 3, 2, 2, 44, 44, 2, 2, 16, 16, 2, 2, 3, 4, 2, 2, 5, 5, 2, 2, 3, 3, 2, 2, 89, 9, 2, 2, 3, 3, 2, 2, 97, 97, 2, 2, 7
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OFFSET
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1,1
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LINKS
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EXAMPLE
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a(1)=2, since binomial(1+2, 2) mod 2 = 3 mod 2 = 1 and 2 is the minimal number with this property.
a(7)=9 because of binomial(7+9, 9) = 11440 = 1271*9 + 1, but binomial(7+k, k) mod k <> 1 for all numbers < 9.
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MATHEMATICA
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Table[Block[{m = 1}, While[Mod[Binomial[n + m, m], m] != 1, m++]; m], {n, 98}] (* Michael De Vlieger, Jul 30 2018 *)
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PROG
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(PARI) a(n) = {my(m = 1, ok = 0); until (ok, if (binomial(n+m, m) % m == 1, ok = 1, m++); ); return (m); } \\ Michel Marcus, Jul 15 2013
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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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