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A117877 Least p=prime(k) for which A118123(k)=n.

%I A117877 #8 Jul 15 2012 09:13:22
%S A117877 2,5,11,17,67,101,109,107,227,569,499,821,1163,2153,1489,1487,1579,
%T A117877 4111,6841,10739,5783,21383,4729,3467,34183,58741,19319,22283,22279,
%U A117877 22277,16069,16067,17333,91583,20479,20477,82223,158363,31189,70877,45061
%N A117877 Least p=prime(k) for which A118123(k)=n.
%e A117877 a(0)=2 because no k exists and it is the least of the three {2, 3 & 7} in A117563 or A117078.
%e A117877 a(1)=5 because 5 + 5 (mod 3) = 7,
%e A117877 a(2)=11 because 11 + 11 (mod 3) = 11 + 11 (mod 9) = 13.
%e A117877 a(3)=17 because 17 + 17 (mod 3) = 17 + 17 (mod 5) = 17 + 17 (mod 15) = 19,
%e A117877 a(4)=67 because 67 + 67 (mod 7) = 67 + 67 (mod 9) = 67 + 67 (mod 21) = 67 + 67 (mod 63) = 71,
%e A117877 a(5)=101 because 101 + 101 (mod 3) = 101 + 101 (mod 9) = 101 + 101 (mod 11) = 101 + 101 (mod 33) = 101 + 101 (mod 99), etc.
%t A117877 f[n_] := Block[{p = Prime@n, np = Prime[n + 1]}, Length@ Select[ Divisors[2p - np], # >= np - p &]]; t = Table[0, {50}]; Do[ a = f@n; If[a < 50 && t[[a + 1]] == 0, t[[a + 1]] = n; Print[{a, n, Prime@n}]], {n, 100000}]
%o A117877 (PARI) A117877(n)={ for( k=n+1, 1e9, n==A118123(k) & return(prime(k)))}
%Y A117877 Cf. A118123, A117078, A117563.
%K A117877 nonn
%O A117877 0,1
%A A117877 _Rémi Eismann_ and _Robert G. Wilson v_, May 14 2006
%E A117877 Edited by _M. F. Hasler_, Nov 07 2009