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Search: id:A003558
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| A003558 |
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Least number m such that 2^m = +- 1 mod 2n + 1. |
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+0
7
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| 0, 1, 2, 3, 3, 5, 6, 4, 4, 9, 6, 11, 10, 9, 14, 5, 5, 12, 18, 12, 10, 7, 12, 23, 21, 8, 26, 20, 9, 29, 30, 6, 6, 33, 22, 35, 9, 20, 30, 39, 27, 41, 8, 28, 11, 12, 10, 36, 24, 15, 50, 51, 12, 53, 18, 36, 14, 44, 12, 24, 55, 20, 50, 7, 7, 65, 18, 36, 34, 69, 46, 60, 14, 42, 74, 15, 24, 20
(list; graph; listen)
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OFFSET
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0,3
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COMMENT
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Multiplicative suborder of 2 (mod 2n+1) (or sord(2, 2n+1)).
For the complexity of computing this, see A002326.
It appears that under iteration of the base-n Kaprekar map, for even n > 2 (A165012, A165051, A165090, A151949 in bases 4, 6, 8, 10), almost all cycles are of length a(n/2 - 1); proved under the additional constraint that the cycle contains at least one element satisfying "number of digits (n-1) - number of digits 0 = o(total number of digits)". [From Joseph Myers (jsm(AT)polyomino.org.uk), Sep 05 2009]
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REFERENCES
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H. Cohen, Course in Computational Algebraic Number Theory, Springer, 1993, p. 25, Algorithm 1.4.3
V. I. Levenshtein, Conflict-avoiding codes and cyclic triple systems [in Russian], Problemy Peredachi Informatsii, 43 (No. 3, 2007), 39-53.
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LINKS
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T. D. Noe, Table of n, a(n) for n = 0..1000
H. J. Smith, XICalc - Extra Precision Integer Calculator.
Eric Weisstein's World of Mathematics, Link to a section of The World of Mathematics, Multiplicative Order.
S. Wolfram, Algebraic Properties of Cellular Automata (1984), Appendix B.
Eric Weisstein's World of Mathematics, Math World: Suborder Function
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MATHEMATICA
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Suborder[a_, n_] := If[n>1 && GCD[a, n]==1, Min[MultiplicativeOrder[a, n, {-1, 1}]], 0]; Table[Suborder[2, 2n+1], {n, 0, 100}] - T. D. Noe (noe(AT)sspectra.com), Aug 02 2006
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CROSSREFS
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a(n) = log_2(A160657(n) + 2) - 1 [From Nathaniel Johnston (nathaniel(AT)nathanieljohnston.com), May 22 2009]
Sequence in context: A023160 A085312 A046530 this_sequence A141419 A072451 A023156
Adjacent sequences: A003555 A003556 A003557 this_sequence A003559 A003560 A003561
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KEYWORD
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nonn
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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 Harry J. Smith (hjsmithh(AT)sbcglobal.net), Feb 11 2005
Entry revised by N. J. A. Sloane (njas(AT)research.att.com), Aug 02 2006
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