A117921 Primes of the form (2^k - 1)^3 - 2.

3373, 29789, 133432829, 8577357821, 281462092005373

Offset: 1

Author

Jonathan Vos Post, May 03 2006

Keywords

• nonn

Comments

Exponent-3 analog of what for exponent 2 is A091516 Carol primes (2^n-1)^2 - 2 = 4^n - 2^{n+1} - 1. Hence this is a type of "near-cube primes."

Examples

			a(1) = (2^4 - 1)^3 - 2 = 3373 is prime.
a(2) = (2^5 - 1)^3 - 2 = 29789 is prime.
a(3) = (2^9 - 1)^3 - 2 = 133432829 is prime.
a(4) = (2^11 - 1)^3 - 2 = 8577357821 is prime.
		

Links

• Charles R Greathouse IV, Table of n, a(n) for n = 1..10
• Eric Weisstein's World of Mathematics, Near-Square Prime.

Crossrefs

Cf. A091516, A091515, A098878, A091514.

Programs

Mathematica

Select[(2^Range[20]-1)^3-2,PrimeQ] (* Harvey P. Dale, Oct 22 2016 *)

Formula

A098878 INTERSECTION A000040. {(2^k - 1)^3 - 2 iff prime}.