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%I #20 Dec 02 2017 10:14:21
%S 1,2,2,3,2,3,2,4,3,2,3,3,2,4,3,3,2,3,3,2,3,4,3,4,3,2,3,2,5,4,4,3,2,4,
%T 2,3,3,5,3,3,2,9,2,3,2,4,5,3,2,5,3,2,7,3,3,3,2,3,3,2,4,4,3,2,4,8,3,5,
%U 2,4,3,4,3,3,5,3,5,4,5,4,2,5,2,3,4,3,5,3,2,4,4,4,5,7,4,3,6,2,4,3,4,3,3,2,3
%N a(n) is the smallest positive integer such that (the n-th prime)+a(n)! is prime, or -1 if no such prime exists.
%C A175194(n) = a(n)!.
%H Michael De Vlieger, <a href="/A175193/b175193.txt">Table of n, a(n) for n = 1..10000</a>
%H Michael De Vlieger, <a href="/A175193/a175193.txt">First positions of values and records in a(n).</a>
%F A092789(n) = A000040(n) + a(n)!.
%e From _Michael De Vlieger_, Nov 24 2017: (Start)
%e Records and their indices in a(n):
%e i n a(n)
%e --------------------
%e 1 1 1
%e 2 2 2
%e 3 4 3
%e 4 8 4
%e 5 29 5
%e 6 42 9
%e 7 233 10
%e 8 254 42
%e 9 4508 49
%e 10 7003 124
%e 11 7385 276
%e 12 60650 311
%e 13 97146 542
%e (End)
%t Fold[Append[#1, SelectFirst[Range[12], Function[k, PrimeQ[Prime[#2] + k!]]]] &, {1}, Range[2, 105]] (* _Michael De Vlieger_, Nov 24 2017 *)
%o (PARI) a(n) = {my(k = 1, p = prime(n)); while (!isprime(p + k!), k++); k;} \\ _Michel Marcus_, Nov 25 2017
%Y Cf. A082470, A092789, A175194.
%K nonn
%O 1,2
%A _Leroy Quet_, Mar 01 2010
%E Extended by _Ray Chandler_, Mar 04 2010
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