A225057 Least prime p such that p*6^n +/- 1 are primes.

2, 2, 2, 2, 47, 3, 53, 677, 823, 227, 1907, 1103, 17, 163, 2693, 1213, 277, 2767, 887, 8353, 1013, 773, 6967, 1423, 2593, 9643, 157, 18013, 263, 2137, 2837, 107, 3467, 2137, 17, 2777, 1453, 2683, 7963, 3517, 2767, 53527, 8563, 227, 367, 27673, 30853, 5087, 7723, 14753, 41687, 137, 48647, 26357, 16747, 2797, 9887, 35933

Offset

1,1

Comments

a(1) >= A064215(n). First n's such that a(n) = A064215(n): 2, 3, 4, 6, 13, 27, 29, 32, 35, 40, 44, 45, 52, 60, 67, 71, 79, 86, 87, 97, 99.

According to Dickson's Conjecture a(n) exists for any n.

Links

Table of n, a(n) for n=1..58.

Chris Caldwell, Prime Glossary: Dickson's Conjecture

Mathematica

Table[ n6=6^n; p = 2; While[ ! PrimeQ[q = p*n6 + 1 ] || ! PrimeQ[ q - 2 ], p = NextPrime[p] ]; p, {n, 100}]

Crossrefs

Cf. A064215 (least k: k*6^n +/- 1 are primes).

Sequence in context: A289087 A378134 A154288 * A084954 A226281 A217993

Adjacent sequences: A225054 A225055 A225056 * A225058 A225059 A225060

Keyword

nonn

Author

Zak Seidov, Apr 26 2013

Status

approved