|
| |
|
|
A014657
|
|
Numbers n that divide 2^k + 1 for some k.
|
|
6
| |
|
|
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; 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. [From Michael 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]
|
|
|
REFERENCES
| P. Moree, Appendix to V. Pless et al., Cyclic Self-Dual Z_4 Codes, Finite Fields Applic., vol. 3 pp. 48-69, 1997.
|
|
|
LINKS
| T. D. Noe, Table of n, a(n) for n=1..1000
|
|
|
MATHEMATICA
| ok[n_] := Module[{k=0}, While[k<=n && Mod[2^k + 1, n] > 0, k++]; k<n]; Select[Range[265], ok] (* From Jean-François Alcover, Apr 06 2011, after PARI prog *)
okQ[n_] := Module[{k = MultiplicativeOrder[2, n]}, EvenQ[k] && Mod[2^(k/2) + 1, n] == 0]; Join[{1, 2}, Select[Range[3, 265, 2], okQ]] (* T. D. Noe, Apr 06 2011 *)
|
|
|
PROG
| (PARI) isA014657(n) = {local(r); r=0; for(k=0, n, if(Mod(2^k+1, n)==Mod(0, n), r=1)); r} [From Michael Porter, Dec 06 2009]
(Haskell)
import Data.List (findIndices)
a014657 n = a014657_list !! (n-1)
a014657_list = map (+ 1) $ findIndices (> 0) $ map a195470 [1..]
-- Reinhard Zumkeller, Sep 21 2011
|
|
|
CROSSREFS
| Cf. A014661.
Cf. A000051.
Sequence in context: A191183 A078645 A067139 * A171056 A161514 A140329
Adjacent sequences: A014654 A014655 A014656 * A014658 A014659 A014660
|
|
|
KEYWORD
| nonn,nice
|
|
|
AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com).
|
|
|
EXTENSIONS
| More terms from Henry Bottomley, May 19 2000. Extended and corrected by David W. Wilson, May 01 2001
|
| |
|
|
