A317851 Primes p such that A090086(p+1) < p.

31, 43, 61, 67, 73, 79, 97, 103, 107, 113, 127, 131, 137, 151, 163, 167, 173, 181, 191, 193, 197, 211, 223, 227, 229, 233, 239, 241, 251, 257, 263, 269, 271, 277, 281, 283, 293, 311, 313, 317, 331, 337, 347, 349, 353, 359, 367, 373, 379, 383, 389, 397, 401, 409, 419, 421

Offset: 1

Author

Thomas Ordowski, Aug 09 2018

Keywords

• nonn

Comments

Theorem: if n-1 is composite, then A090086(n) < n.

The inverse theorem is false iff n = p+1 for primes p in this sequence.

Conjecture: the sequence contains all sufficiently large primes. Probably all primes except 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 37, 41, 47, 53, 59, 71, 83, 89, 101, 109, 139, 149, 157, 179, 199, 307, 461, and 571.

Examples

			The prime 31 is a term, since A090086(31+1) = 25 < 31.
		

Crossrefs

Cf. A000040, A090086.

Programs

PARI

b(n) = {forcomposite(k=2, , if (Mod(n, k)^(k-1) == 1, return (k)); ); }
isok(p) = isprime(p) && (b(p+1) < p); \\ Michel Marcus, Aug 09 2018

Extensions

Corrected and extended by Michel Marcus, Aug 09 2018