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A128457
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Numbers n such that 13^n - 2 is a prime.
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13
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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
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1,2
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COMMENTS
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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
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LINKS
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Table of n, a(n) for n=1..20.
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MATHEMATICA
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Do[ f = 13^n - 2; If[ PrimeQ[ f ], Print[ {n, f} ] ], {n, 1, 1000} ]
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CROSSREFS
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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
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KEYWORD
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hard,more,nonn
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AUTHOR
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Alexander Adamchuk, Mar 14 2007
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EXTENSIONS
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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
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STATUS
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approved
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