

A118534


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


54



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
(list;
graph;
refs;
listen;
history;
text;
internal format)



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]


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(n) = 9 and A117563(5) = 9/3 = 3. Thus 11 has level 3 and so is a member of A117873.


MATHEMATICA

f[n_] := If[n == 1  n == 2  n == 4, 0, 2Prime[n]  Prime[n + 1]]; Array[f, 62] (* Robert G. Wilson v *)


CROSSREFS

Cf. A117078, A117563.
Cf. A117078, A117563, essentially the same as A117563.
Sequence in context: A080407 A197335 A248885 * A187427 A167352 A094472
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



