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 A064164 #23 Jul 08 2024 10:47:53
%S A064164 8,9,13,14,15,16,17,18,19,20,21,22,23,24,26,29,30,31,32,33,34,35,36,
%T A064164 38,39,40,42,43,44,45,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,
%U A064164 63,64,65,66,67,68,69,70,71,72,74,75,76,78,79,80,81,82,83,84,85
%N A064164 EHS numbers: k such that there is a prime p satisfying k! + 1 == 0 (mod p) and p !== 1 (mod k).
%C A064164 The complement of this sequence (A064295) is a superset of A002981, that is, terms of A002981 do not appear in this sequence.
%C A064164 Hardy & Subbarao prove that this sequence is infinite, see their Theorem 2.12. - _Charles R Greathouse IV_, Sep 10 2015
%H A064164 Amiram Eldar, <a href="/A064164/b064164.txt">Table of n, a(n) for n = 1..120</a>
%H A064164 G. E. Hardy and M. V. Subbarao, <a href="http://www.math.ualberta.ca/~subbarao/documents/2002_Pillai.pdf">A modified problem of Pillai and some related questions</a>, Amer. Math. Monthly 109:6 (2002), pp. 554-559.
%H A064164 H. Mishima, <a href="http://www.asahi-net.or.jp/~KC2H-MSM/mathland/matha1/matha104.htm">Factors of N!+1</a>
%t A064164 Do[k = 1; While[p = Prime[k]; k < 10^8 && Not[ Nor[ Mod[n! + 1, p] != 0, Mod[p, n] == 1]], k++ ]; If[k != 10^8, Print[n, " ", p]], {n, 2, 88}]
%o A064164 (PARI) is(n)=my(f=factor(n!+1)[,1]); for(i=1,#f, if(f[i]%n != 1, return(n>1))); 0 \\ _Charles R Greathouse IV_, Sep 10 2015
%Y A064164 The smallest associated primes p are given in A064229.
%Y A064164 Cf. A002981, A064295.
%K A064164 nonn,nice
%O A064164 1,1
%A A064164 _R. K. Guy_, Sep 20 2001
%E A064164 Corrected and extended by _Don Reble_, Sep 23 2001