A274904 Largest prime factor of 6^n + 1.

2, 7, 37, 31, 1297, 101, 97, 197, 98801, 46441, 6781, 51828151, 1678321, 37571, 5030761, 1950271, 4709377, 12690943, 55117, 48713705333, 68754507401, 2527867231, 863017, 990000731, 473896897, 3655688315536801, 6291946695217, 883383463, 81035189089

Offset: 0

Author

Vincenzo Librandi, Jul 11 2016

Keywords

• nonn

Examples

			6^3 + 1 = 217 = 7*31, so a(3) = 31.
		

Links

• Table of n, a(n) for n = 0..430
• J. Brillhart et al., Factorizations of b^n +- 1, Contemporary Mathematics, Vol. 22, Amer. Math. Soc., Providence, RI, 3rd edition, 2002.

Crossrefs

Cf. similar sequences listed in A274903.

Cf. A006530, A062394.

Programs

Magma

[Maximum(PrimeDivisors(6^n+1)): n in [0..40]];

Mathematica

Table[FactorInteger[6^n + 1][[-1, 1]], {n, 0, 40}]

Formula

a(n) = A006530(A062394(n)). - Michel Marcus, Jul 11 2016

Extensions

Terms to a(100) in b-file from Vincenzo Librandi, Jul 12 2016

a(101)-a(408) in b-file from Amiram Eldar, Feb 02 2020

a(409)-a(430) in b-file from Max Alekseyev, Apr 25 2022, Apr 15 2025