This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A298206 #29 Apr 03 2023 10:36:13 %S A298206 6,3,3,6,5,106,207,569,224,736,2854,21234,14837,165394,24743,62721, %T A298206 237804,143332 %N A298206 a(n) is the smallest b >= 2 such that b^(6*2^n) - b^(3*2^n) + 1 is prime. %C A298206 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 %H A298206 Phil Carmody, <a href="http://fatphil.org/maths/PIES/">Prime Internet Eisenstein Search</a> (ca. 2004-2005) %H A298206 Mersenneforum, <a href="http://mersenneforum.org/showthread.php?t=19655">Prime Internet Eisenstein Search discussion</a> %H A298206 The Prime Pages, <a href="https://t5k.org/top20/page.php?id=44">Generalized unique primes</a> %F A298206 a(n) = A085398(18*2^n). - _Jinyuan Wang_, Dec 21 2022 %e A298206 2^12 - 2^6 + 1 = 4033 is composite and 3^12 - 3^6 + 1 = 530713 is prime, so a(1) = 3. %o A298206 (PARI) for(n=0,9,for(b=2,1000,x=b^(3*2^n); if(isprime(x*(x-1)+1), print1(b,", "); break))) %Y A298206 Subsequence of A205506. %Y A298206 Cf. A001620, A085398, A153438, A246119. %K A298206 nonn,hard,more %O A298206 0,1 %A A298206 _Serge Batalov_, Jan 14 2018 %E A298206 a(13) from _Serge Batalov_, Jan 24 2018