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A194591
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Least k >= 0 such that n*2^k - 1 or n*2^k + 1 is prime, or -1 if no such value exists.
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15
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0, 0, 0, 0, 1, 0, 1, 0, 1, 0, 1, 0, 2, 0, 1, 0, 2, 0, 1, 0, 1, 0, 1, 0, 2, 1, 1, 0, 1, 0, 1, 0, 1, 1, 1, 0, 1, 0, 1, 0, 1, 0, 2, 0, 1, 0, 4, 0, 1, 1, 1, 0, 1, 0, 1, 1, 1, 0, 5, 0, 3, 0, 1, 1, 1, 0, 2, 0, 1, 0, 2, 0, 2, 0, 1, 1, 2, 0, 1, 0, 1, 0, 1, 0, 4, 1
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OFFSET
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1,13
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COMMENTS
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Fred Cohen and J. L. Selfridge showed that a(n) = -1 infinitely often.
a(n) = 0 iff n is in A045718.
A217892 and A194600 give indices and values of the records.
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REFERENCES
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Fred Cohen and J. L. Selfridge, Not every number is the sum or difference of two prime powers, Math. Comput. 29 (1975), 79-81.
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LINKS
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Arkadiusz Wesolowski, Table of n, a(n) for n = 1..1000
Eric Weisstein's World of Mathematics, Brier Number
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FORMULA
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If a(n)>0, then a(2n)=a(n)-1.
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EXAMPLE
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For n=7, 7*2^0-1 and 7*2^0+1 are composite, but 7*2^1-1=13 is prime, so a(7)=1.
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MATHEMATICA
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Table[k = 0; While[! PrimeQ[n*2^k - 1] && ! PrimeQ[n*2^k + 1], k++]; k, {n, 100}] (* T. D. Noe, Aug 29 2011 *)
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CROSSREFS
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Cf. A194600, A194603, A194606, A194607, A194608, A194635, A194636, A194637, A194638, A194639.
Cf. A040081, A040076, A076335, A180247.
Sequence in context: A266909 A276491 A035177 * A070105 A111397 A131743
Adjacent sequences: A194588 A194589 A194590 * A194592 A194593 A194594
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KEYWORD
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sign
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AUTHOR
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Arkadiusz Wesolowski, Aug 29 2011
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STATUS
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approved
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