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 A003570 a(n) = least positive number m such that 8^m == +1 or -1 mod 2n + 1, with a(0) = 0 by convention. 0
 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; text; internal format)
 OFFSET 0,3 COMMENTS Multiplicative suborder of 8 (mod 2n+1) = sord(8, 2n+1). - Harry J. Smith, Feb 11 2005 REFERENCES H. Cohen, Course in Computational Algebraic Number Theory, Springer, 1993, p. 25, Algorithm 1.4.3 LINKS Eric Weisstein's World of Mathematics, Multiplicative Order. S. Wolfram, Algebraic Properties of Cellular Automata (1984), Appendix B. EXAMPLE a(1) = 1 since 8^1 = 8 == -1 mod 3. a(2) = 2 since 8^2 = 64 == -1 mod 5. MATHEMATICA Suborder[k_, n_] := If[n > 1 && GCD[k, n] == 1, Min[MultiplicativeOrder[k, n, {-1, 1}]], 0]; a[n_] := Suborder[8, 2 n + 1]; a /@ Range[0, 100] (* Jean-François Alcover, Mar 21 2020, after T. D. Noe in A003558 *) CROSSREFS Sequence in context: A259703 A316996 A169589 * A011281 A300731 A100398 Adjacent sequences:  A003567 A003568 A003569 * A003571 A003572 A003573 KEYWORD nonn AUTHOR EXTENSIONS More terms from Harry J. Smith, Feb 11 2005 Edited by N. J. A. Sloane, May 22 2008 at the suggestion of Jeremy Gardiner STATUS approved

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Last modified November 27 06:29 EST 2021. Contains 349363 sequences. (Running on oeis4.)