A133906 Least number m such that binomial(n+m, m) mod m = 1.

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

Offset: 1

Author

Hieronymus Fischer, Oct 20 2007

Keywords

• nonn

Examples

			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.
		

Links

• Seiichi Manyama, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A000040, A133620, A133621, A133623, A133630, A133635.

Cf. A133872, A133880, A133890, A133900, A133907, A133910.

Programs

Mathematica

Table[Block[{m = 1}, While[Mod[Binomial[n + m, m], m] != 1, m++]; m], {n, 98}] (* Michael De Vlieger, Jul 30 2018 *)

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