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 A283300 #27 Feb 16 2025 08:33:42 %S A283300 2,5,11,109,509,4099,2951209 %N A283300 Primes p such that p^2 divides Bell(p) - 2. %C A283300 A special case of Touchard's congruence is Bell(p) == 2 (mod p) for all primes p, where Bell(n) are the Bell numbers (A000110). These primes are for Touchard's congruence as Wieferich primes (A001220) are for Fermat's little theorem and Wilson primes (A007540) are for Wilson's theorem. %D A283300 J. Touchard, "Propriétés arithmétiques de certains nombres récurrents", Ann. Soc. Sci. Bruxelles A 53 (1933), pp. 21-31. %H A283300 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/TouchardsCongruence.html">Touchard's Congruence</a> %e A283300 For n=3, a(3)=11, Bell(11)=678570, Bell(11) - 2 = 11^2 * 61688. %t A283300 Select[Prime[Range[1000]], Divisible[BellB[#]-2, #^2] &] %Y A283300 Cf. A000110 (Bell numbers). %K A283300 nonn,hard,more,nice %O A283300 1,1 %A A283300 _Amiram Eldar_, Mar 04 2017 %E A283300 a(7) from _Hiroaki Yamanouchi_, Aug 30 2018