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.

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

1,1

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

Links

Table of n, a(n) for n=1..28.

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

Formula

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

Example

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

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 *)

Prog

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

Crossrefs

Cf. A005563, A055932.

Sequence in context: A290283 A163420 A155489 * A045396 A155779 A337815

Adjacent sequences: A194096 A194097 A194098 * A194100 A194101 A194102

Keyword

nonn,more

Author

Vladimir Shevelev, Aug 15 2011

Status

approved