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A099905 a(n) = binomial(2n-1, n-1) mod n. 8
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 (list; graph; refs; listen; history; text; internal format)
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 A085391

Adjacent sequences:  A099902 A099903 A099904 * A099906 A099907 A099908

KEYWORD

nonn,easy

AUTHOR

Henry Bottomley, Oct 29 2004

STATUS

approved

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Last modified September 23 14:40 EDT 2021. Contains 347618 sequences. (Running on oeis4.)