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Search: id:A014657
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| A014657 |
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Numbers n that divide 2^k + 1 for some k. |
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+0
4
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| 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; listen)
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OFFSET
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1,2
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COMMENT
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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 (michael_b_porter(AT)yahoo.com), Dec 06 2009]
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REFERENCES
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P. Moree, Appendix to V. Pless et al., Cyclic Self-Dual Z_4 Codes, Finite Fields Applic., vol. 3 pp. 48-69, 1997.
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LINKS
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T. D. Noe, Table of n, a(n) for n=1..1000
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PROGRAM
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(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 (michael_b_porter(AT)yahoo.com), Dec 06 2009]
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CROSSREFS
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Cf. A014661.
Sequence in context: A056144 A078645 A067139 this_sequence A161514 A140329 A163292
Adjacent sequences: A014654 A014655 A014656 this_sequence A014658 A014659 A014660
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KEYWORD
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nonn,nice,new
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AUTHOR
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N. J. A. Sloane (njas(AT)research.att.com).
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EXTENSIONS
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More terms from Henry Bottomley (se16(AT)btinternet.com), May 19 2000. Extended and corrected by David W. Wilson (davidwwilson(AT)comcast.net), May 01 2001
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