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 A194591 Least k >= 0 such that n*2^k - 1 or n*2^k + 1 is prime, or -1 if no such value exists. 15
 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 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,13 COMMENTS 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. REFERENCES Fred Cohen and J. L. Selfridge, Not every number is the sum or difference of two prime powers, Math. Comput. 29 (1975), 79-81. LINKS Arkadiusz Wesolowski, Table of n, a(n) for n = 1..1000 Eric Weisstein's World of Mathematics, Brier Number FORMULA If a(n)>0, then a(2n)=a(n)-1. EXAMPLE 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. MATHEMATICA Table[k = 0; While[! PrimeQ[n*2^k - 1] && ! PrimeQ[n*2^k + 1], k++]; k, {n, 100}] (* T. D. Noe, Aug 29 2011 *) CROSSREFS 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 KEYWORD sign AUTHOR Arkadiusz Wesolowski, Aug 29 2011 STATUS approved

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Last modified October 22 18:17 EDT 2019. Contains 328319 sequences. (Running on oeis4.)