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

Author

Mike Oakes, Feb 23 2001

Keywords

• nonn
• nice
• hard

Comments

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

Links

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

Crossrefs

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

Programs

Mathematica

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

PARI

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