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Search: id:A057192
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| A057192 |
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Least m such that 1+prime(n)*2^m is a prime, or -1 if no such m exists. |
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+0
5
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| 0, 1, 1, 2, 1, 2, 3, 6, 1, 1, 8, 2, 1, 2, 583, 1, 5, 4, 2, 3, 2, 2, 1, 1, 2, 3, 16, 3, 6, 1, 2, 1, 3, 2, 3, 4, 8, 2, 7, 1, 1, 4, 1, 2, 15, 2, 20, 8, 11, 6, 1, 1, 36, 1, 279, 29, 3, 4, 2, 1, 30, 1, 2, 9, 4, 7, 4, 4, 3, 10, 21, 1, 12, 2, 14, 6393, 11, 4, 3, 2, 1, 4, 1, 2, 6, 1, 3, 8, 5, 6, 19, 3, 2, 1, 2, 5
(list; graph; listen)
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OFFSET
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1,4
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COMMENT
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Primes p such that p*2^m+1 is composite for all m are called Sierpinski numbers. The smallest known prime Sierpinski number is 271129. Currently, 10223 is the smallest prime whose status is unknown.
For 0 < k < a(n), prime(n)*2^k is a nontotient. See A005277. - T. D. Noe, Sep 13 2007
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REFERENCES
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See A046067
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LINKS
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T. D. Noe, Table of n, a(n) for n=1..1000
Ray Ballinger and Wilfrid Keller, Sierpinski Problem
Seventeen or Bust, A Distributed Attack on the Sierpinski problem
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EXAMPLE
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a(8)=6 because prime(8)=19 and the first prime in the sequence 1+19*{2,4,8,16,32,64}={39,77,153,305,609,1217} is 1217=1+19*2^6.
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MATHEMATICA
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Table[p=Prime[n]; k=0; While[ ! PrimeQ[1+p*2^k], k++ ]; k, {n, 100}] (Noe)
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CROSSREFS
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Cf. A058887, A058811, A058812, A002202, A014197, A005277, A005384, A005385, A051686.
Cf. A046067 (least k such that (2n-1)*2^k+1 is prime).
Sequence in context: A075758 A125596 A132405 this_sequence A078777 A135938 A079210
Adjacent sequences: A057189 A057190 A057191 this_sequence A057193 A057194 A057195
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KEYWORD
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nonn
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AUTHOR
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Labos E. (labos(AT)ana.sote.hu), Jan 10 2001
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EXTENSIONS
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Corrected by T. D. Noe (noe(AT)sspectra.com), Aug 03 2005
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