A074476 Largest prime factor of 3^n + 1.

2, 2, 5, 7, 41, 61, 73, 547, 193, 37, 1181, 661, 6481, 398581, 16493, 271, 21523361, 1021, 530713, 101917, 42521761, 2269, 570461, 23535794707, 769, 22996651, 4795973261, 19927, 647753, 5385997, 47763361, 22434744889, 926510094425921

Offset: 0

Author

Rick L. Shepherd, Aug 23 2002

Keywords

• nonn

Links

• Table of n, a(n) for n = 0..691
• S. S. Wagstaff, Jr., The Cunningham Project

Crossrefs

Cf. A006530, A034472, A074477 (largest prime factor of 3^n - 1), A002587 (largest prime factor of 2^n + 1), A074478 (largest prime factor of 5^n + 1).

Programs

Magma

[Maximum(PrimeDivisors(3^n+1)): n in [0..40]]; // Vincenzo Librandi, Aug 23 2013

Mathematica

Table[FactorInteger[3^n + 1][[-1, 1]], {n, 0, 40}] (* Vincenzo Librandi, Aug 23 2013 *)

PARI

for(n=0,35, v=factor(3^n+1); print1(v[matsize(v)[1],1],","))

Formula

a(n) = A006530(A034472(n)). - Amiram Eldar, Feb 01 2020

Extensions

Terms to a(100) in b-file from Vincenzo Librandi, Aug 23 2013

a(101)-a(658) in b-file from Amiram Eldar, Feb 01 2020

a(659)-a(691) in b-file from Max Alekseyev, Apr 25 2022, Jul 25 2023