A066975 a(n) = gcd(binomial(2n,n), 2^n + 1).

1, 1, 1, 1, 1, 3, 1, 3, 1, 1, 1, 3, 17, 1, 5, 9, 1, 3, 5, 3, 1, 3, 5, 3, 1, 3, 1, 1, 17, 3, 41, 1, 1, 3, 5, 129, 1, 1, 5, 1, 1, 3, 5, 3, 17, 9, 5, 3, 1, 3, 1, 9, 1, 3, 5, 3, 1, 3, 5, 3, 17, 3, 1, 3, 1, 33, 5, 3, 1, 9, 115825, 3, 97, 3, 5, 99, 1, 129, 5, 3, 1, 1, 5, 3, 17, 11, 5, 3, 1, 3, 35425, 1, 1

Offset

0,6

Links

Alois P. Heinz, Table of n, a(n) for n = 0..10000 (terms n = 1..1000 from Harry J. Smith)

Formula

a(n) = gcd(A000984(n), A000051(n)).

Maple

a:= n-> igcd(binomial(2*n, n), 2^n+1):
seq(a(n), n=0..92);  # Alois P. Heinz, May 08 2026

Mathematica

Table[GCD[Binomial[2n, n], 2^n+1], {n, 100}] (* Harvey P. Dale, Aug 26 2012 *)

Prog

(PARI) a(n) = { gcd(binomial(2*n, n), 2^n + 1) } \\ Harry J. Smith, Apr 12 2010
(Python)
from math import gcd, comb
def A066975(n): return gcd(comb(n<<1, n), (1<<n)+1) # Chai Wah Wu, May 07 2026

Crossrefs

Cf. A000051, A000984.

Sequence in context: A100375 A353063 A274613 * A355879 A291634 A098877

Adjacent sequences: A066972 A066973 A066974 * A066976 A066977 A066978

Keyword

nonn

Author

Benoit Cloitre, Jan 26 2002

Extensions

a(0)=1 prepended by Alois P. Heinz, May 08 2026

Status

approved