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 A014657 Numbers m that divide 2^k + 1 for some k. 9
 1, 2, 3, 5, 9, 11, 13, 17, 19, 25, 27, 29, 33, 37, 41, 43, 53, 57, 59, 61, 65, 67, 81, 83, 97, 99, 101, 107, 109, 113, 121, 125, 129, 131, 137, 139, 145, 149, 157, 163, 169, 171, 173, 177, 179, 181, 185, 193, 197, 201, 205, 209, 211, 227, 229, 241, 243, 249, 251, 257, 265 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS Since for some a < n, 2^a == 1 (mod n) (a consequence of Euler's Theorem), searching up to k=n is sufficient to determine whether an integer is in the sequence. - Michael B. Porter, Dec 06 2009 A195470(a(n)) > 0; A195610(n) gives the smallest k such that a(n) divides 2^k + 1. - Reinhard Zumkeller, Sep 21 2011 This sequence is the subset of odd integers > 1 as (2*n - 1) in A179480, such that the corresponding entry in A179480 is odd. Example: A179480(14) = 5, odd, with (2*14 - 1) = 27; and 5 is a term of this sequence. A014659 (odd and does not divide (2^k + 1) for any k > 1) represents the subset of odd terms >1 corresponding to A179480 entries that are even. - Gary W. Adamson, Aug 20 2012 All prime factors of a(n) are in A091317.  Sequence has asymptotic density 0. - Robert Israel, Aug 12 2014 This sequence, for m>2, is those m for which, for some e, (m-1)(2^e-1)/m is a term of A253608. Moreover, e(n) is 2*A195610(n) when m is a(n). - Donald M Davis, Jan 12 2018 LINKS T. D. Noe, Table of n, a(n) for n = 1..1000 P. Moree, Appendix to V. Pless et al., Cyclic Self-Dual Z_4 Codes, Finite Fields Applic., vol. 3 pp. 48-69, 1997. MAPLE select(t -> [msolve(2^x+1, t)] <> [], [2*i+1 \$ i=1..1000]); # Robert Israel, Aug 12 2014 MATHEMATICA ok[n_] := Module[{k=0}, While[k<=n && Mod[2^k + 1, n] > 0, k++]; k 0) \$ map a195470 [1..] -- Reinhard Zumkeller, Sep 21 2011 CROSSREFS Besides initial terms 1 and 2, a subsequence of A296243. Their set difference is given by A296244. Cf. A000051, A003558, A014659, A014661, A091317, A179480, A195470, A195610. Sequence in context: A191183 A078645 A067139 * A171056 A161514 A215779 Adjacent sequences:  A014654 A014655 A014656 * A014658 A014659 A014660 KEYWORD nonn,nice AUTHOR EXTENSIONS More terms from Henry Bottomley, May 19 2000 Extended and corrected by David W. Wilson, May 01 2001 STATUS approved

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Last modified December 6 04:14 EST 2019. Contains 329784 sequences. (Running on oeis4.)