A118534 a(n) is the largest k such that prime(n+1) = prime(n) + (prime(n) mod k), or 0 if no such k exists.

0, 0, 3, 0, 9, 9, 15, 15, 17, 27, 25, 33, 39, 39, 41, 47, 57, 55, 63, 69, 67, 75, 77, 81, 93, 99, 99, 105, 105, 99, 123, 125, 135, 129, 147, 145, 151, 159, 161, 167, 177, 171, 189, 189, 195, 187, 199, 219, 225, 225, 227, 237, 231, 245, 251, 257, 267, 265, 273, 279

Offset: 1

Author

Rémi Eismann, Apr 18 2006, Feb 14 2008

Keywords

• nonn
• easy

Comments

a(n) = prime(n) - g(n) or A000040(n) - A001223(n) if prime(n) - g(n) > g(n), 0 otherwise.

a(n) = 0 only for primes 2, 3 and 7.

Under the twin prime conjecture prime(n+1)-prime(n) = 2 infinitely often, and from that we can conclude that k=prime(n)-2 infinitely often. [Roderick MacPhee, Jul 24 2012]

a(n) = A062234(n) for 5 <= n <= 1000. - Georg Fischer, Oct 28 2018

Examples

			n=5: prime(5) = 11, prime(6) = 13, 13 = 11 + (11 mod 3) = 11 + (11 mod 9), so A117078(5) = 3, a(5) = 9 and A117563(5) = 9/3 = 3. Thus 11 has level 3 and so is a member of A117873.
		

Links

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

Crossrefs

Cf. A062234, A117078; essentially the same as A117563.

Programs

Mathematica

a[n_] := If[n == 1 || n == 2 || n == 4, 0, 2Prime[n] - Prime[n + 1]]; Array[a, 62] (* Robert G. Wilson v, May 09 2006 *)

Extensions

Edited by N. J. A. Sloane, May 07 2006

More terms from Robert G. Wilson v, May 09 2006