

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.


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
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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



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



KEYWORD

nonn,easy


AUTHOR



EXTENSIONS



STATUS

approved



