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 A307532 #28 Apr 29 2019 15:32:46
%S A307532 5,7,29,281,65617,4294967681,18446744073709552577,
%T A307532 340282366920938463463374607431768211841,
%U A307532 115792089237316195423570985008687907853269984665640564039457584007913129642241
%N A307532 a(n) is the smallest k > 2^(2^n)+1 such that 2^(k-1) == 1 (mod (2^(2^n)-1)*k).
%C A307532 a(n) is smallest k > 2^(2^n)+1 such that k == 1 (mod 2^n) and 2^(k-1) == 1 (mod k), so a(n) is an odd prime or a Fermat pseudoprime to base 2.
%C A307532 a(n) is the least k = 2^(2^n) + m*2^n + 1 for m > 0 such that 2^(k-1) == 1 (mod k).
%C A307532 The values of m = (a(n)-2^(2^n)-1)/2^n are 2, 1, 3, 3, 5, 12, 15, 3, 9, 202, 56, 304, 635, 11095, 8948, ...; is m = A307535(n) for all n > 4?
%C A307532 Conjecture: a(n) is prime for all n >= 0.
%F A307532 a(n) == 1 (mod 2^n).
%t A307532 a[n_] := Module[{k = 2^(2^n) + 2}, While[PowerMod[2, k - 1, (2^(2^n) - 1)*k] != 1, k++]; k]; Array[a, 10, 0]
%o A307532 (PARI) a(n) = my(k=2^(2^n)+2); while( Mod(2, (2^(2^n)-1)*k)^(k-1) != 1, k++); k; \\ _Michel Marcus_, Apr 25 2019
%Y A307532 Cf. A001567, A065091, A307512, A307535.
%K A307532 nonn
%O A307532 0,1
%A A307532 _Amiram Eldar_ and _Thomas Ordowski_, Apr 13 2019
%E A307532 a(8) from _Chai Wah Wu_, Apr 29 2019