A144360 Primes of the form 8^k + 7. Also, primes of the form 64^m + 7.

71, 262151, 1073741831, 302231454903657293676551, 85070591730234615865843651857942052871, 23945242826029513411849172299223580994042798784118791, 25711008708143844408671393477458601640355247900524685364822023

Offset: 1

Author

Reikku Kulon, Sep 18 2008

Keywords

• nonn

Comments

k=2m, since for odd k, 8^k + 7 is divisible by 3.

Prime numbers p in A144242 such that p-1 is the fourth a-gonal and seventh b-gonal number for some a and b. Namely, a = (8^k+14)/6 and b = (8^k + 41)/21.

This sequence appears to be a subset of A144313.

The next term has 178 digits. - Harvey P. Dale, Sep 03 2015

Examples

			71 - 1 = 70 is the fourth triskaidecagonal number and seventh pentagonal number.
		

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10

Crossrefs

Cf. A000040, A000668, A144231, A144232, A144233, A144234, A144236, A144242, A144245, A144246, A144247, A144313.

Programs

Magma

[a: n in [0..80] | IsPrime(a) where a is 8^n+7]; // Vincenzo Librandi, Aug 02 2017

Mathematica

Select[64^Range[40]+7,PrimeQ] (* Harvey P. Dale, Sep 03 2015 *)

Formula

a(n) = A253211(A217381(n)). - Amiram Eldar, Jul 23 2025

Extensions

Edited by Max Alekseyev, Feb 17 2011