A340996 a(n) is the number of different primes that can be expressed as n mod p where p < n is prime.

0, 0, 0, 0, 1, 0, 1, 2, 1, 1, 1, 2, 2, 2, 1, 3, 2, 3, 2, 3, 1, 3, 2, 5, 2, 4, 2, 4, 3, 4, 3, 3, 4, 3, 1, 6, 3, 4, 2, 6, 3, 6, 3, 5, 4, 5, 4, 7, 4, 6, 4, 5, 3, 8, 3, 5, 3, 6, 4, 9, 3, 6, 5, 8, 4, 7, 2, 6, 4, 8, 4, 9, 5, 7, 5, 8, 3, 9, 5, 7, 7, 7, 4, 10, 5, 6, 5, 7, 6, 12, 5, 7, 7, 7, 4, 11, 5, 9

Offset: 1

Author

J. M. Bergot and Robert Israel, Feb 01 2021

Keywords

• nonn
• look

Comments

a(n) is the number of primes p < n such that n-p has a prime factor > p.

a(n) <= A056172(n-1), with equality for n = 1, 2, 3, 4, 5, 8, 24.

Examples

			a(8) = 2 because 2 = 8 mod 3 and 3 = 8 mod 5.
		

Links

• Robert Israel, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A056172, A340997.

Programs

Maple

f:= proc(n) local k; nops(select(isprime,{seq(n mod k, k=select(isprime,[$2..n-1]))})) end proc:
map(f, [$1..100]);