A345706 a(n) is the least exponent k > 0 of the n-th prime such that (Product_{j=1..n-1} prime(j)) * prime(n)^k + 1 is a Euclid-Pocklington prime (A053341).

1, 1, 2, 2, 3, 6, 5, 12, 9, 8, 10, 9, 20, 14, 24, 18, 12, 16, 58, 26, 20, 30, 42, 322, 276, 27, 25, 48, 27, 208, 38, 77, 48, 55, 414, 94, 67, 107, 53, 33, 56, 38, 34, 52, 60, 60, 483, 41, 155, 105, 43, 476, 68, 126, 51, 387, 49, 121, 46, 65, 395, 68, 78, 308

Offset: 1

Author

Amiram Eldar, Jun 24 2021

Keywords

• nonn

Comments

The corresponding primes are 3, 7, 151, 1471, 279511, 11149928791, 42638305711, 1129919399332465852111, ...

Examples

			a(1) = 1 since prime(1) = 2, 2^1 > 1 and 2 + 1 = 3 is a prime.
a(2) = 1 since prime(2) = 3, 3^1 > 2 and 2*3 + 1 = 7 is a prime.
a(3) = 2 since prime(3) = 5, 5^2 > 2*3 and 2*3*5^2 + 1 = 151 is a prime.
		

Crossrefs

Cf. A053341.

Programs

Mathematica

a[n_] := Module[{r = Product[Prime[j], {j, 1, n - 1}], p = Prime[n], k}, k = Max[1, Ceiling @ Log[p, r]]; While[!PrimeQ[r*p^k + 1], k++]; k]; Array[a, 64]