A180640 Primes P such that P < (largest prime factor of (P-1)) * (largest prime factor of (P+1)).

2, 3, 5, 11, 13, 23, 29, 37, 43, 47, 59, 61, 67, 73, 83, 103, 107, 113, 131, 137, 139, 149, 157, 167, 173, 179, 193, 211, 223, 227, 229, 233, 263, 269, 277, 281, 283, 293, 311, 313, 317, 331, 347, 353, 359, 367, 373, 383, 389, 397, 409, 421, 439, 443, 457, 467

Offset: 1

Author

Karl Hovekamp, Sep 14 2010

Keywords

• nonn

Examples

			For n = 3, a(3)=11.
The prime P = 11
P-1 = 10 (largest prime factor of 10 is 5)
P+1 = 12 (largest prime factor of 12 is 3)
11 < 5*3.
		

Crossrefs

Cf. A180641. See also A103666, A103667.

Programs

Mathematica

Select[Prime[Range[100]],#<(FactorInteger[#-1][[-1,1]] FactorInteger[#+1][[-1,1]])&]  (* Harvey P. Dale, Feb 22 2011 *)

PARI

isok(p) = (p==2) || (isprime(p) && (p < vecmax(factor(p-1)[, 1]) * vecmax(factor(p+1)[, 1]))); \\ Michel Marcus, Oct 29 2022

Extensions

Initial term, i.e., 2, added by Harvey P. Dale, Feb 22 2011