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

1,3

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

Links

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

Example

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.

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 *)

Crossrefs

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

Sequence in context: A080407 A197335 A248885 * A187427 A167352 A318303

Adjacent sequences: A118531 A118532 A118533 * A118535 A118536 A118537

Keyword

nonn,easy

Author

Rémi Eismann, Apr 18 2006, Feb 14 2008

Extensions

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

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

Status

approved