A128457 Numbers k such that 13^k - 2 is a prime.

1, 2, 4, 5, 12, 78, 80, 90, 117, 120, 813, 1502, 2306, 2946, 6308, 13320, 26369, 31868, 44265, 81008

Offset: 1

Author

Alexander Adamchuk, Mar 14 2007

Keywords

• nonn
• hard
• more

Comments

13320 is a term found by Lelio R Paula 11/2006.

Numbers corresponding to a(13)..a(16) are probable primes. If n is of the form 4k+3 then 13^n-2 is composite, because 13^n-2 == (3^4)^k*3^3 - 2 == 25 == 0 (mod 5). So there is no term of the form 4k+3. - Farideh Firoozbakht, Dec 07 2009

a(21) > 2*10^5. - Robert Price, Oct 03 2014

Crossrefs

Cf. A084714 (smallest prime of the form (2n-1)^k - 2).

Cf. A128472 (smallest prime of the form (2n-1)^k - 2 for k > (2n-1)).

Cf. A014224, A109080, A090669, A128455, A128458, A128459, A128460, A128461.

Programs

Mathematica

Do[ f = 13^n - 2; If[ PrimeQ[ f ], Print[ {n, f} ] ], {n,1,1000} ]

Extensions

813 from Stefan Steinerberger, May 05 2007

a(12) from M. F. Hasler, Feb 07 2009

a(13)-a(16) from Farideh Firoozbakht, Dec 07 2009

a(17)-a(20) from Robert Price, Oct 03 2014