A110905 a(n) is the least number k such that k*prime(n)# - 1 is prime and (k*prime(n)# - 1)^2 - 2 is a Chen prime.

2, 1, 1, 11, 1, 6, 41, 17, 8, 13, 14, 107, 84, 23, 4, 101, 13, 89, 211, 58, 83, 75, 260, 414, 35, 39, 871, 79, 27, 42, 915, 44, 349, 142, 249, 404, 140, 84, 1068, 693, 972, 236, 1571, 1200, 298, 423, 970, 183, 173, 659, 523, 645, 1596, 448, 40, 201, 195, 1859, 427, 1732

Offset: 1

Author

Pierre CAMI, Sep 21 2005

Keywords

• nonn

Examples

			2*2-1 = 3, (2*2-1)^2-2 = 7, 3 and 7 are primes, so a(1) = 2.
11*2*3*5*7-1 = 2309, (11*2*3*5*7-1)^2-2 = 5331479, 2309 and 5331479 are primes, so a(4) = 11.
		

Crossrefs

Cf. A002110, A109611.

Programs

Mathematica

chenQ[n_] := PrimeQ[n] && PrimeOmega[n+2] <= 2; a[n_] := Module[{p = Product[Prime[i], {i, 1, n}], k = 0}, While[!PrimeQ[k*p - 1] || !chenQ[(k*p-1)^2-2], k++]; k]; Array[a, 60] (* Amiram Eldar, Sep 11 2021 *)

PARI

isok(k, q) = if (isprime(k*q-1), my(c=(k*q-1)^2-2); (isprime(c) && (bigomega(c+2)<=2)));
a(n) = my(k=1, q=prod(i=1, n, prime(i))); while (!isok(k, q), k++); k; \\ Michel Marcus, Sep 11 2021