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A005417 Maximal period of an n-stage shift register.
(Formerly M1587)
1
2, 6, 12, 30, 60, 120, 210, 420, 840, 1260, 2520, 2520, 5040, 9240, 13860, 27720, 32760, 55440, 65520, 120120, 180180, 360360, 360360, 720720, 720720, 942480, 1113840 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,1
COMMENTS
Maximal order of an element of finite order in GL(2n, Z) or GL(2n+1, Z).
a(n) is the max of the first n numbers in A080742.
REFERENCES
H. Lüneburg, Galoisfelder, Kreisteilungskörper und Schieberegisterfolgen. B. I. Wissenschaftsverlag, Mannheim, 1979.
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
LINKS
J. Kuzmanovich and A. Pavlichenkov, Finite groups of matrices whose entries are integers, Amer. Math. Monthly, 109 (2002), 173-186.
FORMULA
a(n) = max m such that A067240(m) <= 2n + 1. E.g., a(2) = 12 since 12 is largest m such that A067240(m) <= 5.
MATHEMATICA
(* b, c = a080737 *)
nmax = 26;
kmax = 1200000; (* kmax increased by 100000 until results do not change *)
b[1] = b[2] = 0; b[p_?PrimeQ] := b[p] = p-1; b[k_] := b[k] = If[Length[f = FactorInteger[k]]==1, EulerPhi[k], Total[b /@ (f[[All, 1]]^f[[All, 2]])] ];
orders = Table[{k, b[k]}, {k, 1, kmax}];
c[0] = 2; c[n_] := c[n] = Select[orders, 2n-1 <= #[[2]] <= 2n&][[-1, 1]];
a[n_] := Table[c[m], {m, 0, n}] // Max;
Table[a[n], {n, 0, nmax}] (* Jean-François Alcover, Dec 17 2017 *)
CROSSREFS
Sequence in context: A284573 A355475 A080742 * A058215 A330542 A166456
KEYWORD
nonn,nice,more
AUTHOR
EXTENSIONS
Entry revised by N. J. A. Sloane, Mar 10 2002
STATUS
approved

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Last modified March 19 03:33 EDT 2024. Contains 370952 sequences. (Running on oeis4.)