A014659 Odd numbers that do not divide 2^k + 1 for any k >= 1.

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

Offset: 1

Author

N. J. A. Sloane

Keywords

• nonn

Comments

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

From Wolfdieter Lang, Aug 22 2020: (Start)

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)

Links

• T. D. Noe, Table of n, a(n) for n = 1..1000
• P. Moree, Appendix B, to V. Pless et al., Cyclic Self-Dual Z_4 Codes, Finite Fields Applic., vol. 3 pp. 48-69, 1997.

Crossrefs

Cf. A179480, A002326, A003558, A201908, A332433.

Cf. A014657, numbers that divide 2^k + 1 for some k.

Extensions

More terms from Don Reble, Nov 03 2001