A129736 -id:A129736 - 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

A129737 List of primitive prime divisors of the numbers 4^n-3^n (A005061) in their order of occurrence.

Original entry on oeis.org

7, 37, 5, 11, 71, 13, 14197, 337, 6553, 181, 23, 174659, 193, 131, 500111, 379, 61, 601, 17, 4241, 17050729021, 19, 163, 10814953, 25309, 8861, 8352709, 727, 859, 47, 44483, 17389, 1933, 51361, 1440528320401, 313, 31357, 36174709, 2053, 29, 376853, 59, 349

Offset: 1

N. J. A. Sloane, May 13 2007

nonn

Read A005061 term-by-term, factorize each term, write down any primes not seen before.

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, A129736, A059801, A129733.

cp's OEIS Frontend

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

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