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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 (list; graph; refs; listen; history; text; internal format)
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^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

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 (2n-1)^k - 2, or 0 if no such number exists. Cf. A128472 = smallest prime of the form (2n-1)^k - 2 for k>(2n-1), 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

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Last modified January 18 16:27 EST 2020. Contains 331011 sequences. (Running on oeis4.)