Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).
%I #43 Nov 11 2016 07:42:08
%S 3,5,7,11,17,19,29,31,41,49,71,161,251,449,769,881,1079,1429,3431,
%T 4159,4801,6049,8749,19601,24751,246401,388961,1267111
%N Numbers m>=2, such that, if a prime p divides m^2-1, then every prime q<p divides m^2-1 as well.
%C No more terms <= 10^8.
%C No more terms <= 2 * 10^38. [_Charles R Greathouse IV_, Aug 22 2011]
%C All terms are odd. - _Kausthub Gudipati_, Aug 22 2011
%H Florian Luca and Filip Najman, <a href="https://web.math.pmf.unizg.hr/~fnajman/FLFNMC.pdf">On the largest prime factor of x^2 - 1.</a> Math. Comp. 80 (2011), 429-435.
%F A055932 INTERSECT A005563. - _R. J. Mathar_, Aug 16 2011
%e 881^2-1 = 776160 = 2^5 * 3^2 * 5 *7^2 * 11 (all primes <= 11 appear), so 881 is a term.
%t Select[Range[1, 10^4], First@ # == 1 && If[Length@ # > 1, Union@ Differences@ # == {1}, True] &@ PrimePi@ Map[First, FactorInteger[#^2 - 1]] &] (* _Michael De Vlieger_, Jul 02 2016 *)
%o (PARI) isok(n) = my(f = factor(n^2-1)); #f~ == primepi(f[#f~,1]); \\ _Michel Marcus_, Jul 02 2016
%Y Cf. A005563, A055932.
%K nonn,more
%O 1,1
%A _Vladimir Shevelev_, Aug 15 2011