

A128457


Numbers n such that 13^n  2 is a prime.


13



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

1,2


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^n2 is composite. Because 13^n2==(3^4)^k*3^32==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


LINKS

Table of n, a(n) for n=1..20.


MATHEMATICA

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


CROSSREFS

Cf. A084714 = smallest prime of the form (2n1)^k  2, or 0 if no such number exists. Cf. A128472 = smallest prime of the form (2n1)^k  2 for k>(2n1), or 0 if no such number exists. Cf. A014224, A109080, A090669, A128455, A128458, A128459, A128460, A128461.
Sequence in context: A050599 A281643 A102932 * A139485 A079407 A078652
Adjacent sequences: A128454 A128455 A128456 * A128458 A128459 A128460


KEYWORD

hard,more,nonn


AUTHOR

Alexander Adamchuk, Mar 14 2007


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


STATUS

approved



