A274905 Largest prime factor of 8^n + 1.

2, 3, 13, 19, 241, 331, 109, 5419, 673, 87211, 1321, 20857, 38737, 22366891, 14449, 18837001, 22253377, 43691, 279073, 160465489, 4562284561, 77158673929, 4327489, 168749965921, 487824887233, 1133836730401, 21841, 272010961, 88959882481, 96076791871613611

Offset: 0

Author

Vincenzo Librandi, Jul 11 2016

Keywords

• nonn

Links

• Table of n, a(n) for n = 0..502
• J. Brillhart et al., Factorizations of b^n +- 1, Contemporary Mathematics, Vol. 22, Amer. Math. Soc., Providence, RI, 3rd edition, 2002.

Crossrefs

Cf. A002587, A006530, A062395.

Cf. similar sequences listed in A274903.

Programs

Magma

[Maximum(PrimeDivisors(8^n+1)): n in [0..40]];

Maple

8^4 + 1 = 4097 = 17*241, so a(4) = 241.

Mathematica

Table[FactorInteger[8^n + 1][[-1, 1]], {n, 0, 40}]

Formula

a(n) = A006530(A062395(n)). - Michel Marcus, Jul 11 2016

a(n) = A002587(3*n). - Amiram Eldar, Feb 02 2020

Extensions

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

a(101)-a(354) in b-file from Amiram Eldar, Feb 02 2020

a(355)-a(502) in b-file from Max Alekseyev, May 28 2022, Sep 06 2022, Feb 25 2023