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Search: id:A019567
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| A019567 |
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a(n) is least number m for which either 2^m + 1 or 2^m - 1 is divisible by 4n + 1. |
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+0
1
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| 1, 2, 3, 6, 4, 6, 10, 14, 5, 18, 10, 12, 21, 26, 9, 30, 6, 22, 9, 30, 27, 8, 11, 10, 24, 50, 12, 18, 14, 12, 55, 50, 7, 18, 34, 46, 14, 74, 24, 26, 33, 20, 78, 86, 29, 90, 18, 18, 48, 98, 33, 10, 45, 70, 15, 24, 60, 38, 29, 78, 12, 84, 41, 110, 8, 84, 26, 134, 12, 46, 35, 36, 68, 146
(list; graph; listen)
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OFFSET
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0,2
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COMMENT
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Write down 1, then 2 to left, 3 to right, 4 to left, ..., getting [ 2n,2n-2,...,4,2,1,3,5,...,2n-1 ]; the sequence 2,3,6,4,6,10,14,5,18,10,12,21,26,9,... gives order of permutation sending 1 to 2n, 2 to 2n-2, ..., 2n to 2n-1.
Equivalently, the sequence 2,3,6,4,6,10,14,5,18,10,12,21,26,9,... gives the number of Mongean shuffles needed to return a deck of 2n cards (n=1,2,3,...) to its original order.
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REFERENCES
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A. P. Domoryad, Mathematical Games and Pastimes, Pergamon Press, 1964; see pp. 134-135.
W. W. Rouse Ball, Mathematical Recreations and Essays, 11th ed. 1939, p. 311.
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EXAMPLE
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Illustrating the initial terms:
n 4n+1 2^m+1 2^m-1 m
0..1...........1...1
1..5.....5.........2
2..9.....9.........3
3.13...5*13........6
4.17.....17........4
5.21..........3*21.6
6.25..41*25.......10
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MAPLE
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(Crude Maple program from njas, Jul 28 2007)
f:=proc(n) local m;
for m from 1 to 500 do
if 2^m-1 mod (4*n+1) = 0 then RETURN(m); fi;
if 2^m+1 mod (4*n+1) = 0 then RETURN(m); fi;
od:
-1;
end;
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CROSSREFS
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Sequence in context: A127915 A072637 A125703 this_sequence A098286 A138608 A092283
Adjacent sequences: A019564 A019565 A019566 this_sequence A019568 A019569 A019570
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KEYWORD
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nonn,easy
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AUTHOR
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John Bullitt (metta(AT)world.std.com), njas and J. H. Conway (conway(AT)math.princeton.edu)
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EXTENSIONS
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Comments corrected by Mikko Nieminen, Jul 26 2007, who also provided the Domoryad reference.
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