A129737 -id:A129737 - cp's OEIS frontend

A059801 Numbers k such that 4^k - 3^k is prime.

2, 3, 7, 17, 59, 283, 311, 383, 499, 521, 541, 599, 1193, 1993, 2671, 7547, 24019, 46301, 48121, 68597, 91283, 131497, 148663, 184463, 341233

Offset: 1

Mike Oakes, Feb 23 2001

Some of the larger entries may only correspond to probable primes.
The values corresponding to 1193 (719 digits) and 1993 (1200 digits) have been certified prime with Primo. - Rick L. Shepherd, Sep 10 2002
8 more terms found by Jean-Louis Charton during 2004 - 2006. Corresponding numbers of decimal digits are 14461, 27876, 28972, 41300, 54958, 79170, 89505, 111058, 205443. - Alexander Adamchuk, Dec 02 2006

Bogley, William A.; Williams, Gerald Efficient finite groups arising in the study of relative asphericity. Math. Z. 284, No. 1-2, 507-535 (2016).

Cf. A000043, A057468, A059802, etc., A129736, A129737.

Select[Range[1000], PrimeQ[4^# - 3^#] &] (* Alonso del Arte, Nov 03 2011 *)

select(vector(10^5,i,i),n->ispseudoprime(4^n-3^n)) \\ Charles R Greathouse IV, Feb 11 2011

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

Original entry on oeis.org

7, 37, 14197, 17050729021, 332306984815842876487217260305275077

Offset: 1

N. J. A. Sloane, May 13 2007

nonn

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.

Cf. A005061, A059801, A129733, A129737.

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

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

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

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

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

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

cp's OEIS Frontend

A059801 Numbers k such that 4^k - 3^k is prime.

Views

Author

Keywords

Comments

Links

Crossrefs

Programs

Mathematica

PARI