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A003569
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For n>0, a(n) = least positive number m such that 4^m == +1 or -1 (mod 2n + 1), with a(0) = 0 by convention.
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0
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0, 1, 1, 3, 3, 5, 3, 2, 2, 9, 3, 11, 5, 9, 7, 5, 5, 6, 9, 6, 5, 7, 6, 23, 21, 4, 13, 10, 9, 29, 15, 3, 3, 33, 11, 35, 9, 10, 15, 39, 27, 41, 4, 14, 11, 6, 5, 18, 12, 15, 25, 51, 6, 53, 9, 18, 7, 22, 6, 12, 55, 10, 25, 7, 7, 65, 9, 18, 17, 69, 23, 30, 7, 21, 37, 15, 12, 10, 13, 26, 33, 81, 10
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OFFSET
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0,4
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COMMENTS
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Multiplicative suborder of 4 (mod 2n+1) = sord(4, 2n+1). - Harry J. Smith, Feb 11 2005
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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
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LINKS
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MATHEMATICA
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lpn[n_]:=Module[{m=1, pm}, pm=PowerMod[4, m, 2n+1]; While[pm!=1 && pm != 2n, m++; pm=PowerMod[4, m, 2n+1]]; m]; Join[{0}, Array[lpn, 90]] (* Harvey P. Dale, May 22 2016 *)
Suborder[k_, n_] := If[n > 1 && GCD[k, n] == 1, Min[MultiplicativeOrder[k, n, {-1, 1}]], 0];
a[n_] := Suborder[4, 2 n + 1];
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CROSSREFS
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KEYWORD
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easy,nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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