1,1

Exponent 4 analogue of what for exponent 2 is A091516 Carol primes (2^n-1)^2 - 2 = 4^n - 2^{n+1} - 1, and exponent 3 is A098878 (2^n - 1)^3 - 2. Primes include a(n) for n = 0, 2, 3, 11, 57; a type of "near-biquadratic primes." No more primes through (2^100-1)^4 - 2. Semiprimes include a(n) for n = 5, 6, 8, 10, 13, 14, 19, 20, 21, 25, 33, 35, 36, 40, 43, 51, 53, 63.

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

a(n) = (2^n - 1)^4 - 2.

a(0) = (2^0 - 1)^4 - 2 = 0^4 - 2 = -2 which is technically prime (although not in the positive restriction A000040).

a(1) = (2^1 - 1)^4 - 2 = 1^4 - 2 = -1.

a(2) = (2^2 - 1)^4 - 2 = 3^4 - 2 = 79 is prime.

a(3) = (2^3 - 1)^4 - 2 = 7^4 - 2 = 2399 is prime.

a(11) = (2^11 - 1)^4 - 2 = 17557851463679 is prime

a(57) = (2^57 - 1)^4 - 2 = 431359146674410224742050828377557509468732765984721170947417969786879 is prime.

Cf. A091516, A091515, A098878, A091514.

Sequence in context: A096681 A067276 A118580 this_sequence A095837 A095835 A141527

Adjacent sequences: A118555 A118556 A118557 this_sequence A118559 A118560 A118561

easy,sign

Jonathan Vos Post (jvospost3(AT)gmail.com), May 03 2006