A099905 a(n) = binomial(2n-1, n-1) mod n.

0, 1, 1, 3, 1, 0, 1, 3, 1, 8, 1, 2, 1, 10, 0, 3, 1, 12, 1, 10, 3, 14, 1, 6, 1, 16, 10, 0, 1, 2, 1, 3, 21, 20, 21, 26, 1, 22, 10, 10, 1, 0, 1, 24, 0, 26, 1, 30, 1, 28, 27, 48, 1, 30, 16, 44, 48, 32, 1, 48, 1, 34, 6, 35, 35, 0, 1, 18, 33, 20, 1, 18, 1, 40, 60, 16, 0, 72, 1, 10, 10, 44, 1, 56, 75

Offset: 1

Author

Henry Bottomley, Oct 29 2004

Keywords

• nonn
• easy

Comments

For p prime, a(p)=1. For n in A058008, a(n)=0.

For n the square of a prime p>=3 or the cube of a prime p>=5, a(n)=1. - Franz Vrabec, Mar 26 2008

For n in A228562, a(n)=1. - Felix Fröhlich, Oct 17 2015

Examples

			a(11) = 352716 mod 11 = 1.
		

Links

• Felix Fröhlich, 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).

Crossrefs

Cf. A058008, A088218, A099906, A099907, A099908, A228562.

Programs

Magma

[Binomial(2*n-1,n-1) mod n : n in [1..100]]; // Wesley Ivan Hurt, Oct 17 2015

Maple

A099905:=n->binomial(2*n-1,n-1) mod n: seq(A099905(n), n=1..100); # Wesley Ivan Hurt, Oct 17 2015

Mathematica

Table[Mod[Binomial[2n-1,n-1],n],{n,90}] (* Harvey P. Dale, Dec 12 2011 *)

PARI

a(n) = lift(Mod(binomial(2*n-1, n-1), n)) \\ Felix Fröhlich, Oct 17 2015