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 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 (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] 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

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Last modified October 6 12:35 EDT 2022. Contains 357264 sequences. (Running on oeis4.)