A054758 a(n) is the smallest multiplier w such that A002110(n)*w + prime(n+1)^2 is prime.

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, 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, 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

Offset: 1

Author

Labos Elemer, Apr 25 2000

Keywords

• nonn

Comments

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.

Examples

			2310 + 169 = 2479 = 37*67 = 2*3*5*7*11 + 13^2 is not prime but 2*2310 + 169 = 4789 is a prime.
		

Links

• Michael De Vlieger, Table of n, a(n) for n = 1..500

Crossrefs

Cf. A002110.

Programs

Mathematica

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 *)

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