A129736 Primes of the form 4^k - 3^k.

7, 37, 14197, 17050729021, 332306984815842876487217260305275077

Offset: 1

Author

N. J. A. Sloane, May 13 2007

Keywords

• nonn

Links

• Muniru A Asiru, Table of n, a(n) for n = 1..13
• Bogley, William A.; Williams, Gerald Efficient finite groups arising in the study of relative asphericity. Math. Z. 284, No. 1-2, 507-535 (2016).
• G. Everest et al., Primes generated by recurrence sequences, Amer. Math. Monthly, 114 (No. 5, 2007), 417-431.
• K. Zsigmondy, Zur Theorie der Potenzreste, Monatsh. Math., 3 (1892), 265-284.

Crossrefs

Cf. A005061, A059801, A129733, A129737.

Programs

GAP

Filtered(List([1..100], n -> 4^n-3^n), IsPrime); # Muniru A Asiru, Feb 09 2018

Magma

[a: n in [0..300] | IsPrime(a) where a is 4^n-3^n]; // Vincenzo Librandi, Nov 23 2010

Maple

select(isprime, [seq(4^n - 3^n, n=0..100)]); # Muniru A Asiru, Feb 09 2018

Mathematica

fQ[n_] := If[PrimeQ[4^n - 3^n], 4^n - 3^n, Nothing]; Array[fQ, 300] (* Robert G. Wilson v, Feb 12 2018 *)

PARI

lista(nn) = for(k=1, nn, if(isprime(p=4^k-3^k), print1(p", "))) \\ Altug Alkan, Mar 03 2018

Formula

a(n) = A005061(A059801(n)). - Michel Marcus, Feb 12 2018