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%I #19 Jun 11 2021 08:40:20
%S 1,2,4,5,12,78,80,90,117,120,813,1502,2306,2946,6308,13320,26369,
%T 31868,44265,81008
%N Numbers k such that 13^k - 2 is a prime.
%C 13320 is a term found by Lelio R Paula 11/2006.
%C 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
%C a(21) > 2*10^5. - _Robert Price_, Oct 03 2014
%t Do[ f = 13^n - 2; If[ PrimeQ[ f ], Print[ {n, f} ] ], {n,1,1000} ]
%Y Cf. A084714 (smallest prime of the form (2n-1)^k - 2).
%Y Cf. A128472 (smallest prime of the form (2n-1)^k - 2 for k > (2n-1)).
%Y Cf. A014224, A109080, A090669, A128455, A128458, A128459, A128460, A128461.
%K nonn,hard,more
%O 1,2
%A _Alexander Adamchuk_, Mar 14 2007
%E 813 from _Stefan Steinerberger_, May 05 2007
%E a(12) from _M. F. Hasler_, Feb 07 2009
%E a(13)-a(16) from _Farideh Firoozbakht_, Dec 07 2009
%E a(17)-a(20) from _Robert Price_, Oct 03 2014
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