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, 787061080478274202283, 3148244321913096809131

Offset: 2

Author

Artur Jasinski, Feb 09 2007

Keywords

• nonn

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

Examples

			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.
		

Links

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

Crossrefs

Cf. A000040, A000979, A000978, A001045, A124400.

Programs

Magma

[(2^NthPrime(n)+1)/3: n in [2..20]]; // Vincenzo Librandi, Mar 29 2012

Mathematica

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

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

Formula

a(n) = A001045(A000040(n)). - Alois P. Heinz, Apr 14 2025