A066827 a(n) = gcd(2^((n*(n+1)/2)) + 1, 2^n + 1).

3, 1, 1, 1, 33, 1, 1, 1, 513, 1, 1, 1, 8193, 1, 1, 1, 131073, 1, 1, 1, 2097153, 1, 1, 1, 33554433, 1, 1, 1, 536870913, 1, 1, 1, 8589934593, 1, 1, 1, 137438953473, 1, 1, 1, 2199023255553, 1, 1, 1, 35184372088833, 1, 1, 1, 562949953421313, 1, 1, 1

Offset

1,1

Links

Harry J. Smith, Table of n, a(n) for n = 1..500

Formula

If n is not congruent to 1 mod 4, a(n) = 1. If n is congruent to 1 mod 4, a(n) = 2^n + 1.

G.f.: (-16x^5-2x^2+3x)/(16x^4-1)/(x-1). - Ralf Stephan, Mar 12 2003

Mathematica

Table[If[Mod[n, 4]==1, 2^n+1, 1], {n, 80}] (* Harvey P. Dale, Jun 30 2022 *)

Prog

(PARI) a(n) = { gcd(2^((n*(n+1)/2)) + 1, 2^n + 1) } \\ Harry J. Smith, Mar 30 2010

Crossrefs

Sequence in context: A320412 A286591 A297557 * A016467 A342275 A324049

Adjacent sequences: A066824 A066825 A066826 * A066828 A066829 A066830

Keyword

nonn

Author

Benoit Cloitre, Jan 20 2002

Status

approved