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 A378143 #13 Dec 03 2024 12:43:37 %S A378143 5,17,257,65537,808551180810136214718004658177, %T A378143 9807585394417153072393128067370344132933540474708183331242417216238928121991128579833857 %N A378143 a(n) is the smallest prime of the form (2*p)^(2^n) + 1 for some prime p. %C A378143 If p = 2, then a(n) is the Fermat prime. %C A378143 Conjecture: the last digit of each value of a(n), where n >= 1, is 7. %C A378143 The conjecture is equivalent to the claim that a(n) is not 10^(2^n) + 1 for any n, which in turn is equivalent to the claim that, if 10^(2^n) + 1 is prime, then either 4^(2^n) + 1 or 6^(2^n) + 1 is prime. - _Charles R Greathouse IV_, Nov 17 2024 %Y A378143 Primes p such that (2*p)^(2^k) + 1 is prime: A005384 (k = 0), A052291 (k = 1), A378146 (k = 2). %Y A378143 Cf. A019434, A222008, A286678, A378134. %K A378143 nonn %O A378143 0,1 %A A378143 _Juri-Stepan Gerasimov_, Nov 17 2024