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A014659
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Odd numbers that do not divide 2^k + 1 for any k >= 1.
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4
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7, 15, 21, 23, 31, 35, 39, 45, 47, 49, 51, 55, 63, 69, 71, 73, 75, 77, 79, 85, 87, 89, 91, 93, 95, 103, 105, 111, 115, 117, 119, 123, 127, 133, 135, 141, 143, 147, 151, 153, 155, 159, 161, 165, 167, 175, 183, 187, 189, 191, 195, 199, 203, 207, 213, 215, 217, 219
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OFFSET
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1,1
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COMMENTS
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This is the subset of odd integers > 1 as (2*n - 1) in A179480 such that A179480(n) is even. Example: A179480(18) = 6, even; corresponding to (2*18 - 1), 35. Then 35 is in A014659. A014657 is the subset of odd terms > 1 corresponding to odd terms in A179480. - Gary W. Adamson, Aug 20 2012
These odd numbers are the moduli named 2*n+1 in the definition of A003558(n), for n >= 1, for which the + sign applies. The signs in the definition of A003558 are given in A332433.
These are the odd numbers N >= 3 for which A003558((N-1)/2) = A002326((N+1)/2), the period length P(N) of the cycles {2^k (mod N)}_{k=0}^(P(N)-1). Compare the periods given in A201908((N+1)/2, k). (End)
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LINKS
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P. Moree, Appendix B, to V. Pless et al., Cyclic Self-Dual Z_4 Codes, Finite Fields Applic., vol. 3 pp. 48-69, 1997.
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CROSSREFS
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Cf. A014657, numbers that divide 2^k + 1 for some k.
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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