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%I #17 Nov 20 2017 03:30:40
%S 1,1,1,1,2,1,2,3,2,8,5,4,1,6,3,13,7,2,1,6,2,3,5,7,7,8,31,1,22,6,60,20,
%T 12,5,2,12,5,16,7,20,1,2,14,42,23,16,13,30,53,5,7,36,10,10,67,6,2,40,
%U 24,3,28,59,6,4,76,1,74,5,30,16,2,39,6,56,138,3,22,37,11,8,35,102,156
%N a(n) is the smallest multiplier w such that A002110(n)*w + prime(n+1)^2 is prime.
%C For n=1,2,3,4,6,13,19,28,41,66,85,..., A002110(n) + prime(n+1)^2 is a prime; i.e., the multiplier w is 1.
%H Michael De Vlieger, <a href="/A054758/b054758.txt">Table of n, a(n) for n = 1..500</a>
%e 2310 + 169 = 2479 = 37*67 = 2*3*5*7*11 + 13^2 is not prime but 2*2310 + 169 = 4789 is a prime.
%t Table[Function[{P, q}, w = 1; While[! PrimeQ[P w + q], w++]; w] @@ {Times @@ #2, First[#1]^2} & @@ # &@ TakeDrop[Take[#, n], -1], {n, 2, Length@ #}] &@ Prime@ Range@ 84 (* _Michael De Vlieger_, Jul 14 2017 *)
%o (PARI) a(n) = {my(m=1, primo=prod(k=1, n, prime(k))); while (!isprime(primo*m + prime(n+1)^2), m++); m;} \\ _Michel Marcus_, Nov 20 2017
%Y Cf. A002110.
%K nonn
%O 1,5
%A _Labos Elemer_, Apr 25 2000
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