A133346 a(n) = smallest k such that prime(n+2) = prime(n) + (prime(n) mod k), or 0 if no such k exists.

0, 0, 0, 0, 0, 7, 11, 0, 15, 21, 21, 31, 7, 11, 35, 9, 17, 17, 61, 9, 21, 23, 23, 77, 7, 19, 97, 101, 91, 19, 13, 41, 25, 127, 47, 139, 21, 17, 31, 11, 167, 13, 37, 11, 61, 25, 39, 7, 13, 73, 9, 227, 25, 239, 35, 15, 9, 29, 271, 269, 37, 25, 7, 61, 59, 27, 21, 13, 11, 113, 113

Offset: 1

Author

Rémi Eismann, Oct 20 2007

Keywords

• nonn

Examples

			For n = 1 we have prime(n) = 2, prime(n+2) = 5; there is no k such that 5 - 2 = 3 = (2 mod k), hence a(1) = 0.
For n = 6 we have prime(n) = 13, prime(n+2) = 19; 7 is the smallest k such that 19 - 13 = 6 = (13 mod k), hence a(6) = 7.
For n = 30 we have prime(n) = 113, prime(n+2) = 131; 19 is the smallest k such that 131 - 113 = 18 = (113 mod k), hence a(30) = 19.
		

Links

• Remi Eismann, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A000040, A117078, A117563, A001223, A118534, A020639, A090369, A090368, A130533, A130650, A130703, A130889, A130882.