A126614 a(n) = (2^prime(n) + 1)/3.

3, 11, 43, 683, 2731, 43691, 174763, 2796203, 178956971, 715827883, 45812984491, 733007751851, 2932031007403, 46912496118443, 3002399751580331, 192153584101141163, 768614336404564651, 49191317529892137643

Offset

2,1

Comments

If p - 1 is squarefree, the multiplicative order of 2 modulo a(n) is 2p. - Vladimir Shevelev, Jul 15 2008

The prime numbers in this sequence are the Wagstaff primes (A000979). - Omar E. Pol, Nov 05 2013

Links

Vincenzo Librandi, Table of n, a(n) for n = 2..200

Example

a(2) = (2^prime(2) + 1)/3 = (2^3 + 1)/3 = 9/3 = 3.
a(3) = (2^prime(3) + 1)/3 = (2^5 + 1)/3 = 33/3 = 11.
a(4) = (2^prime(4) + 1)/3 = (2^7 + 1)/3 = 129/3 = 43.

Mathematica

Table[(2^Prime[n] + 1)/3, {n, 2, 20}]

Prog

(Magma) [(2^NthPrime(n)+1)/3: n in [2..20]]; // Vincenzo Librandi, Mar 29 2012
(PARI) a(n)=2^prime(n)\/3 \\ Charles R Greathouse IV, Mar 29 2012
(PARI) vecextract(apply(p->2^p\/3, primes(100)), "2..") \\ Charles R Greathouse IV, Mar 29 2012

Crossrefs

Cf. A000040, A000979, A000978, A124400.

Sequence in context: A051257 A135482 A360475 * A000979 A123628 A153476

Adjacent sequences: A126611 A126612 A126613 * A126615 A126616 A126617

Keyword

nonn

Author

Artur Jasinski, Feb 09 2007

Status

approved