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Search: id:A087139
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| A087139 |
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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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| 2, 2, 3, 2, 11, 2, 5, 30, 15, 3, 6, 10, 81, 3, 17, 961, 15, 7, 2, 5, 6, 2, 3, 3, 12, 3, 57, 5, 16, 5, 166, 15, 13, 2, 3, 2, 30, 2, 25, 3, 47, 3, 3, 2, 521, 9, 3, 15, 17, 42, 17, 51, 39
(list; graph; listen)
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OFFSET
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1,1
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COMMENT
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The next term in this sequence, a(54) for the prime p=251, is greater than 6700. Is there a prime p such that p^k - p^(k-1) + 1 is composite for all k > 1? For the related question of Sierpinski numbers (n such that n*2^k+1 is composite for all k ), the answer is yes.
The next term in this sequence, a(54), for the prime p=251, is greater than 10698. - Bernardo Boncompagni (redgolpe(AT)redgolpe.com) Jul 03 2004
If n=251^k-251^(k-1)+1 is prime then k mod 10 = 1,5,7 or 9 because n mod 3 = 0 iff k is even and n mod 11 = 0 iff k mod 5 = 3. More exponents can be cleared this way. The next term of this sequence, a(54), for the prime p=251, is greater than 10726. - Bernardo Boncompagni (redgolpe(AT)redgolpe.com), Oct 23 2005
Note that k cannot be 8, 14, 20, ... (i.e. k == 2 mod 6) because then p^2 - p + 1 divides p^k - p^(k-1) + 1. - T. D. Noe (noe(AT)sspectra.com), Aug 31 2006
New limit for next term: a(54)>73000. - T. D. Noe (noe(AT)sspectra.com), Aug 31 2006
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REFERENCES
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See A087126.
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MATHEMATICA
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lst={}; Do[p=Prime[n]; i=2; While[m=p^i-p^(i-1)+1; !PrimeQ[m], i++ ]; AppendTo[lst, i], {n, 53}]; lst
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CROSSREFS
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Cf. A040076 (Sierpinski numbers), A087126 (primes of the form p^k - p^(k-1) + 1).
Cf. A122396.
Adjacent sequences: A087136 A087137 A087138 this_sequence A087140 A087141 A087142
Sequence in context: A016002 A098189 A016003 this_sequence A016005 A016006 A016007
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KEYWORD
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more,nonn
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AUTHOR
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T. D. Noe (noe(AT)sspectra.com), Aug 18 2003
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