A274909 Largest prime factor of 9^n - 1.

2, 5, 13, 41, 61, 73, 1093, 193, 757, 1181, 3851, 6481, 797161, 16493, 4561, 21523361, 34511, 530713, 363889, 42521761, 368089, 570461, 23535794707, 6481, 22996651, 4795973261, 19927, 647753, 20381027, 47763361, 22434744889, 926510094425921, 2413941289

Offset: 1

Author

Vincenzo Librandi, Jul 11 2016

Keywords

• nonn

Examples

			9^4 - 1 = 6560 = 2^5*5*41, so a(4) = 41.
		

Links

• Table of n, a(n) for n = 1..691
• J. Brillhart et al., Factorizations of b^n +- 1, Contemporary Mathematics, Vol. 22, Amer. Math. Soc., Providence, RI, 3rd edition, 2002.

Crossrefs

Cf. A006530, A024101, A074477.

Cf. similar sequences listed in A274906.

Programs

Magma

[Maximum(PrimeDivisors(9^n-1)): n in [1..40]];

Mathematica

Table[FactorInteger[9^n-1][[-1,1]],{n,40}]

Formula

a(n) = A006530(A024101(n)).

a(n) = A074477(2*n). - Amiram Eldar, Feb 02 2020

a(n) = max(A074476(n),A074477(n)). - Max Alekseyev, Apr 25 2022

Extensions

Terms to a(100) in b-file from Vincenzo Librandi, Jul 13 2016

a(101)-a(330) in b-file from Amiram Eldar, Feb 02 2020

a(331)-a(691) in b-file from Max Alekseyev, May 22 2022, Jul 25 2023