A059801 - OEIS

A059801

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

120

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

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OFFSET

1,1

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

Table of n, a(n) for n=1..25.

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

MATHEMATICA

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

PROG

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

CROSSREFS

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

Sequence in context: A176074 A281368 A330726 * A102226 A195530 A295509

Adjacent sequences: A059798 A059799 A059800 * A059802 A059803 A059804

KEYWORD

nonn,nice,hard

AUTHOR

Mike Oakes, Feb 23 2001

STATUS

approved