A317851 - OEIS

%I #15 Aug 11 2018 15:36:14

%S 31,43,61,67,73,79,97,103,107,113,127,131,137,151,163,167,173,181,191,

%T 193,197,211,223,227,229,233,239,241,251,257,263,269,271,277,281,283,

%U 293,311,313,317,331,337,347,349,353,359,367,373,379,383,389,397,401,409,419,421

%N Primes p such that A090086(p+1) < p.

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

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

%C 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.

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

%o (PARI) b(n) = {forcomposite(k=2, , if (Mod(n, k)^(k-1) == 1, return (k)); ); }

%o isok(p) = isprime(p) && (b(p+1) < p); \\ _Michel Marcus_, Aug 09 2018

%Y Cf. A000040, A090086.

%K nonn

%O 1,1

%A _Thomas Ordowski_, Aug 09 2018

%E Corrected and extended by _Michel Marcus_, Aug 09 2018