

A298206


a(n) = smallest b >= 2 such that b^(6*2^n)  b^(3*2^n) + 1 is prime.


1



6, 3, 3, 6, 5, 106, 207, 569, 224, 736, 2854, 21234, 14837, 165394, 24743, 62721, 237804, 143332
(list;
graph;
refs;
listen;
history;
text;
internal format)



OFFSET

0,1


COMMENTS

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 EulerMascheroni 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


LINKS

Table of n, a(n) for n=0..17.
Phil Carmody, Prime Internet Eisenstein Search (ca. 20042005)
Mersenneforum, Prime Internet Eisenstein Search discussion
The Prime Pages, Generalized unique primes


EXAMPLE

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


PROG

(PARI) for(n=0, 9, for(b=2, 1000, x=b^(3*2^n); if(isprime(x*(x1)+1), print1(b, ", "); break)))


CROSSREFS

Subsequence of A205506.
Cf. A001620, A246119, A153438.
Sequence in context: A327773 A085670 A011410 * A023407 A153841 A334843
Adjacent sequences: A298203 A298204 A298205 * A298207 A298208 A298209


KEYWORD

nonn,hard,more


AUTHOR

Serge Batalov, Jan 14 2018


EXTENSIONS

a(13) from Serge Batalov, Jan 24 2018


STATUS

approved



