A263729 Primes p where (p - 1)/k - 1 is not prime for any integer k >= 1.

2, 3, 11, 23, 47, 59, 83, 107, 131, 167, 179, 227, 251, 263, 347, 359, 383, 431, 443, 467, 479, 503, 563, 587, 599, 719, 839, 863, 887, 947, 983, 1019, 1031, 1091, 1187, 1223, 1283, 1307, 1319, 1367, 1439, 1451, 1487

Offset: 1

Author

Juri-Stepan Gerasimov, Oct 24 2015

Keywords

• nonn
• easy

Comments

Primes p such that (p^2 + p*q)/(p + 1) is not integer for all primes q.

Primes p such that d1 - 1, d2 - 1, .. are not primes where d1, d2, .. are all divisors of p - 1.

Examples

			11 is in this sequence because (11 - 1)/1 - 1 = 9, (11 - 1)/2 - 1 = 4, (11 - 1)/5 - 1 = 1, (11 - 1)/10 - 1 = 0 are nonprimes and 11 is prime.
		

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A027750, A263730, A263770.

Programs

PARI

lista(nn) = {forprime (p=2, nn, ok = 1; for (k=1, p-1, x = (p-1)/k - 1; if (denominator(x)==1 && isprime(x), ok = 0; break);); if (ok, print1(p, ", ")););} \\ Michel Marcus, Nov 02 2015

Extensions

Name edited by Franklin T. Adams-Watters, Oct 31 2015