A225192 Number of primes p such that p is -1 mod n where p < n-th prime.

0, 0, 1, 1, 0, 2, 1, 1, 1, 1, 0, 2, 0, 2, 1, 2, 0, 2, 1, 2, 1, 1, 0, 3, 0, 0, 1, 1, 0, 3, 1, 2, 1, 2, 1, 2, 1, 3, 0, 1, 1, 3, 0, 2, 2, 1, 0, 2, 1, 2, 1, 1, 1, 2, 1, 2, 2, 1, 0, 3, 0, 1, 1, 2, 0, 3, 0, 2, 1, 1, 1, 1, 0, 1, 1, 3, 1, 3, 1, 2, 0, 2, 1, 4, 0, 1, 2

Offset: 1

Author

Irina Gerasimova, May 01 2013

Keywords

• nonn

Comments

Primes p(n) such that a(n) = a(n + 1): 2, 5, 17, 19, 23, 73, 97, 103, 173, 193, 233, 239, 263, 293, 347, 349, 353, 373, 449, 467,...

Primes p(n) such that p is not -1 mod n and mod n+1 for all prime p < p(n+1): 2, 97, 829, 1597, 2251,...

Smallest k such that a(k) = n:, 1, 3, 6, 24, 84, 90,...

Numbers n such that a(n) is equal to number of primes p such that n is -1 mod p where p < n-th prime: 1, 2, 3, 4, 7, 8, 10, 14, 15, 20, 22, 28, 31, 32, 34, 40, 44, 45, 46, 50, 52, 55, 57, 63, 65, 70, 72, 87,...

Examples

			Prime 11 == - 1 (mod 12), prime 23 == -1 (mod 12) and 11, 23 < prime(12) = 37, so a(12) = 2.
		

Links

• Charles R Greathouse IV, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A038700, A219109.

Programs

Mathematica

Table[s = Prime[Range[n - 1]]; Length[Select[s, Mod[#, n] == n - 1 &]], {n, 93}] (* T. D. Noe, May 13 2013 *)

PARI

a(n)=my(s); forstep(p=n-1,prime(n)-1,n,s+=isprime(p)); s \\ Charles R Greathouse IV, Mar 18 2014