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A122396
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Least k>1 such that p^k - p^(k-1) - 1 is prime for p = prime(n).
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3
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3, 2, 2, 2, 2, 3, 2, 7, 56, 2, 2, 8, 8, 8, 2, 4, 4, 2, 2, 2, 9, 3, 21496, 26, 2, 2, 4, 38, 7, 286644, 2, 2, 26, 2, 2, 4, 4, 15, 4, 24, 16, 2, 264, 4, 2, 3, 24, 3, 516, 6
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OFFSET
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1,1
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COMMENTS
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Does a(n) always exist? Note that k cannot be 5, 11, 17,... (i.e., k=5 mod 6) because then p^2 - p + 1 divides p^k - p^(k-1) - 1.
From Richard N. Smith, Jul 15 2019: (Start)
The link has the primes 82*83^21495-1 = 83^21496-83^21495-1 and 112*113^286643-1 = 113^286644-113^286643-1, thus a(23)=21496 and a(30)=286644.
a(51) > 250000, since 232*233^k-1 is composite for all k<=250000, see link.
a(52) - a(61) = {4, 2, 80, 14, 76, 2, 90, 6, 80, 769}, a(62) > 200000. (End)
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LINKS
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Table of n, a(n) for n=1..50.
Steven Harvey, Williams primes
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MATHEMATICA
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lst={}; Do[p=Prime[n]; k=2; While[m=p^k-p^(k-1)-1; !PrimeQ[m], k++ ]; AppendTo[lst, k], {n, 22}]; lst
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PROG
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(PARI) a(n)=for(k=2, 10^6, if(ispseudoprime(prime(n)^k - prime(n)^(k-1) - 1), return(k))) \\ Richard N. Smith, Jul 15 2019
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CROSSREFS
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Cf. A087139, A122395.
Sequence in context: A104223 A057934 A058758 * A272893 A037199 A145376
Adjacent sequences: A122393 A122394 A122395 * A122397 A122398 A122399
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KEYWORD
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nonn,more,hard
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AUTHOR
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T. D. Noe, Aug 31 2006
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EXTENSIONS
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a(23)-a(50) from Richard N. Smith, Jul 15 2019, using Steven Harvey's table.
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STATUS
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approved
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