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%I #31 Mar 30 2020 08:43:49
%S 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,
%T 99,99,105,105,99,123,125,135,129,147,145,151,159,161,167,177,171,189,
%U 189,195,187,199,219,225,225,227,237,231,245,251,257,267,265,273,279
%N a(n) is the largest k such that prime(n+1) = prime(n) + (prime(n) mod k), or 0 if no such k exists.
%C a(n) = prime(n) - g(n) or A000040(n) - A001223(n) if prime(n) - g(n) > g(n), 0 otherwise.
%C a(n) = 0 only for primes 2, 3 and 7.
%C 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]
%C a(n) = A062234(n) for 5 <= n <= 1000. - _Georg Fischer_, Oct 28 2018
%H Remi Eismann, <a href="/A118534/b118534.txt">Table of n, a(n) for n = 1..10000</a>
%e 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.
%t 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 *)
%Y Cf. A062234, A117078; essentially the same as A117563.
%K nonn,easy
%O 1,3
%A _Rémi Eismann_, Apr 18 2006, Feb 14 2008
%E Edited by _N. J. A. Sloane_, May 07 2006
%E More terms from _Robert G. Wilson v_, May 09 2006
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