cp's OEIS Frontend

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.

A194099 Numbers m>=2, such that, if a prime p divides m^2-1, then every prime q divides m^2-1 as well.

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%I A194099 #43 Nov 11 2016 07:42:08
%S A194099 3,5,7,11,17,19,29,31,41,49,71,161,251,449,769,881,1079,1429,3431,
%T A194099 4159,4801,6049,8749,19601,24751,246401,388961,1267111
%N A194099 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 A194099 No more terms <= 10^8.
%C A194099 No more terms <= 2 * 10^38. [_Charles R Greathouse IV_, Aug 22 2011]
%C A194099 All terms are odd. - _Kausthub Gudipati_, Aug 22 2011
%H A194099 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 A194099 A055932 INTERSECT A005563. - _R. J. Mathar_, Aug 16 2011
%e A194099 881^2-1 = 776160 = 2^5 * 3^2 * 5 *7^2 * 11 (all primes <= 11 appear), so 881 is a term.
%t A194099 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 A194099 (PARI) isok(n) = my(f = factor(n^2-1)); #f~ == primepi(f[#f~,1]); \\ _Michel Marcus_, Jul 02 2016
%Y A194099 Cf. A005563, A055932.
%K A194099 nonn,more
%O A194099 1,1
%A A194099 _Vladimir Shevelev_, Aug 15 2011