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A003570
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a(n) = least positive number m such that 8^m == +1 or -1 mod 2n + 1, with a(0) = 0 by convention.
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0
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0, 1, 2, 1, 1, 5, 2, 4, 4, 3, 2, 11, 10, 3, 14, 5, 5, 4, 6, 4, 10, 7, 4, 23, 7, 8, 26, 20, 3, 29, 10, 2, 2, 11, 22, 35, 3, 20, 10, 13, 9, 41, 8, 28, 11, 4, 10, 12, 8, 5, 50, 17, 4, 53, 6, 12, 14, 44, 4, 8, 55, 20, 50, 7, 7, 65, 6, 12, 34, 23, 46, 20, 14, 14, 74, 5, 8, 20, 26, 52, 11, 27, 20, 83
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,3
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COMMENTS
| Multiplicative suborder of 8 (mod 2n+1) = sord(8, 2n+1). - Harry J. Smith (hjsmithh(AT)sbcglobal.net), Feb 11 2005
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REFERENCES
| H. Cohen, Course in Computational Algebraic Number Theory, Springer, 1993, p. 25, Algorithm 1.4.3
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LINKS
| 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.
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EXAMPLE
| a(1) = 1 since 8^1 = 8 == -1 mod 3.
a(2) = 2 since 8^2 = 64 == -1 mod 5.
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CROSSREFS
| Sequence in context: A128704 A075259 A169589 * A011281 A100398 A160364
Adjacent sequences: A003567 A003568 A003569 * A003571 A003572 A003573
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KEYWORD
| nonn
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com).
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EXTENSIONS
| More terms from Harry J. Smith (hjsmithh(AT)sbcglobal.net), Feb 11 2005
Edited by N. J. A. Sloane (njas(AT)research.att.com), May 22 2008 at the suggestion of Jeremy Gardiner
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