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

7, 37, 14197, 17050729021, 332306984815842876487217260305275077

Offset

1,1

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.

Formula

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

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 *)

Prog

(Magma) [a: n in [0..300] | IsPrime(a) where a is 4^n-3^n] // Vincenzo Librandi, Nov 23 2010]
(GAP) Filtered(List([1..100], n -> 4^n-3^n), IsPrime); # Muniru A Asiru, Feb 09 2018
(PARI) lista(nn) = for(k=1, nn, if(isprime(p=4^k-3^k), print1(p", "))) \\ Altug Alkan, Mar 03 2018

Crossrefs

Cf. A005061, A059801, A129733, A129737.

Sequence in context: A250843 A078303 A127729 * A220852 A290176 A003352

Adjacent sequences: A129733 A129734 A129735 * A129737 A129738 A129739

Keyword

nonn

Author

N. J. A. Sloane, May 13 2007

Status

approved