A113569 Least number k such that k is a multiple of A034386(2*n) and p-(n-1)*k, p-(n-2)*k, ... p-2*k, p-k, p, p+k, p+2*k, ... p+(n-2)*k, and p+(n-1)*k are all prime, with p being the k-th prime.

2, 6, 720, 252420, 2053380

Offset

1,1

Comments

Without the condition that k must be a multiple of A034386(2*n), we would have a(1) = 1 and a(2) = 4. - Pontus von Brömssen, Jun 25 2025

Links

Table of n, a(n) for n=1..5.

Example

a(1) = 2 which is a multiple of the primorial A034386(2) = 2.
a(2) = 6 because p = 13, p-6 = 7, and p+6 = 19 are all prime and 6 is a multiple of A034386(4) = 6.
a(3) = 720 because p = 5443, p-720 = 4723, p-2*720 = 4003, p+720 = 6163, and p+2*720 = 6883 are all prime and 720 is a multiple of A034386(6) = 30.

Crossrefs

Cf. A034386, A064403, A112530, A113567, A113568.

Sequence in context: A180492 A169661 A047690 * A252739 A178773 A381250

Adjacent sequences: A113566 A113567 A113568 * A113570 A113571 A113572

Keyword

nonn,hard,more

Author

Robert G. Wilson v, Sep 10 2005

Extensions

Edited by Pontus von Brömssen, Jun 25 2025

Status

approved