1,1

Exponent 3 analogue 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." No more primes through (2^100-1)^3 - 2.

Eric Weisstein's World of Mathematics, Near-Square Prime.

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

a(1) = (2^0 - 1)^3 - 2 = (-1)^3 - 2 = -2 which is technically prime (although not in the positive restriction A000040).

a(2) = (2^4 - 1)^3 - 2 = 3373 is prime.

a(3) = (2^5 - 1)^3 - 2 = 29789 is prime.

a(4) = (2^9 - 1)^3 - 2 = 133432829 is prime.

a(5) = (2^11 - 1)^3 - 2 = 8577357821 is prime.

a(6) = (2^16 - 1)^3 - 2 = 281462092005373 is prime.

Cf. A091516, A091515, A098878, A091514.

Sequence in context: A128148 A099689 A065671 this_sequence A094211 A114573 A024035

Adjacent sequences: A117918 A117919 A117920 this_sequence A117922 A117923 A117924

easy,sign

Jonathan Vos Post (jvospost2(AT)yahoo.com), May 03 2006