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

1,4

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

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).

Example

a(11) = 352716 mod 11 = 1.

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 *)

Prog

(PARI) a(n) = lift(Mod(binomial(2*n-1, n-1), n)) \\ Felix Fröhlich, Oct 17 2015
(Magma) [Binomial(2*n-1, n-1) mod n : n in [1..100]]; // Wesley Ivan Hurt, Oct 17 2015

Crossrefs

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

Sequence in context: A120323 A320476 A304326 * A268441 A264435 A356656

Adjacent sequences: A099902 A099903 A099904 * A099906 A099907 A099908

Keyword

nonn,easy

Author

Henry Bottomley, Oct 29 2004

Status

approved