0,1

a(13) = 165394 is a significant outlier from the generally expected trend, which can be conjectured to be 6*2^n*gamma, where gamma is the Euler-Mascheroni constant A001620. Additionally, the next b > a(13) such that b^(6*2^n) - b^(3*2^n) + 1 is prime is 165836, which is remarkably close to a(13). - Serge Batalov, Jan 24 2018

Phil Carmody, Prime Internet Eisenstein Search (ca. 2004-2005)

Mersenneforum, Prime Internet Eisenstein Search discussion

The Prime Pages, Generalized unique primes

a(n) = A085398(18*2^n). - Jinyuan Wang, Dec 21 2022

2^12 - 2^6 + 1 = 4033 is composite and 3^12 - 3^6 + 1 = 530713 is prime, so a(1) = 3.

(PARI) for(n=0, 9, for(b=2, 1000, x=b^(3*2^n); if(isprime(x*(x-1)+1), print1(b, ", "); break)))

Subsequence of A205506.

Cf. A001620, A085398, A153438, A246119.

Sequence in context: A085670 A011410 A356412 * A023407 A153841 A334843

Adjacent sequences: A298203 A298204 A298205 * A298207 A298208 A298209

nonn,hard,more

Serge Batalov, Jan 14 2018

a(13) from Serge Batalov, Jan 24 2018

approved