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

1,3

Comments

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

Links

Table of n, a(n) for n=1..64.

Example

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.

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]

Crossrefs

Cf. A053341.

Sequence in context: A210751 A279791 A328744 * A132886 A119272 A308483

Adjacent sequences: A345703 A345704 A345705 * A345707 A345708 A345709

Keyword

nonn

Author

Amiram Eldar, Jun 24 2021

Status

approved