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

3, 5, 7, 11, 17, 19, 29, 31, 41, 49, 71, 161, 251, 449, 769, 881, 1079, 1429, 3431, 4159, 4801, 6049, 8749, 19601, 24751, 246401, 388961, 1267111

Offset: 1

Author

Vladimir Shevelev, Aug 15 2011

Keywords

• nonn
• more

Comments

No more terms <= 10^8.

No more terms <= 2 * 10^38. [Charles R Greathouse IV, Aug 22 2011]

All terms are odd. - Kausthub Gudipati, Aug 22 2011

Examples

			881^2-1 = 776160 = 2^5 * 3^2 * 5 *7^2 * 11 (all primes <= 11 appear), so 881 is a term.
		

Links

• Florian Luca and Filip Najman, On the largest prime factor of x^2 - 1. Math. Comp. 80 (2011), 429-435.

Crossrefs

Cf. A005563, A055932.

Programs

Mathematica

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 *)

PARI

isok(n) = my(f = factor(n^2-1)); #f~ == primepi(f[#f~,1]); \\ Michel Marcus, Jul 02 2016

Formula

A055932 INTERSECT A005563. - R. J. Mathar, Aug 16 2011