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 A384148 #18 May 28 2025 16:20:58 %S A384148 30457,33865,80185,82621,86785,104845,212401,250705 %N A384148 Numbers k such that (2^k-1)^k == 1 (mod (2^k+1)*k^2) and 2^(k-1) != 1 (mod k). %C A384148 If p > 3 is prime, then (2^p-1)^p == 1 (mod (2^p+1)*p^2). %C A384148 Generally, if m is not divisible by 3 and 2^(m-1) == 1 (mod m), then (2^m-1)^m == 1 (mod (2^m+1)*m^2). %C A384148 However, there are composite numbers satisfying this congruence that are not Fermat pseudoprimes to base 2. These exceptions constitute this sequence. %o A384148 (PARI) isok(k) = if (!isprime(k) && (Mod(2, k)^(k-1) != 1), Mod((2^k-1),(2^k+1)*k^2)^k == 1); \\ _Michel Marcus_, May 20 2025 %Y A384148 Cf. A001567, A066488 (Fermat pseudoprimes to base 2 that are not divisible by 3). %K A384148 nonn,hard,more %O A384148 1,1 %A A384148 _Thomas Ordowski_, May 20 2025 %E A384148 a(3)-a(6) from _Michel Marcus_, May 21 2025 %E A384148 a(7)-a(8) from _Michael S. Branicky_, May 28 2025