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A179382
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a(n) is the smallest period of pseudo-arithmetic progression with initial term 1 and difference 2n-1.
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17
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1, 1, 2, 1, 3, 5, 6, 1, 4, 9, 2, 4, 10, 9, 14, 1, 5, 5, 18, 4, 10, 7, 5, 9, 10, 2, 26, 8, 9, 29, 30, 1, 6, 33, 11, 14, 3, 9, 15, 17, 27, 41, 2, 11, 4, 4, 3, 14, 24, 15, 50, 23, 4, 53, 18, 14, 14, 19, 3, 9, 55, 6, 50, 1, 7, 65, 8, 17, 34, 69, 23, 25, 14, 20, 74, 5, 10, 8, 26, 21
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OFFSET
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1,3
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COMMENTS
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Let x,y be odd numbers. Denote <+> the following binary operation: x<+>y=A000265(x+y). Let a and d be odd numbers. We call sequence of the form b, b<+>d, (b<+>d)<+>d,... a pseudo-arithmetic progression with the initial term b and the difference d. It is not difficult to prove that every pseudo-arithmetic progression is periodic sequence. This sequence lists smallest periods of pseudo-arithmetic progressions with initial term 1 and difference 2n-1, n=1,2,...
A sense of a(n) is: the number of distinct odd residues contained in set {1,2,...,2^(2*n-2)} modulo 2*n-1. Thus 2*n-1 is in A001122 iff a(n)=n-1. - Vladimir Shevelev, Jul 18 2010
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LINKS
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Peter J. C. Moses, Table of n, a(n) for n = 1..4096
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EXAMPLE
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For n=5, we have 1<+>9=5, 5<+>9=7, 7<+>9=1. Thus a(5)=3.
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MAPLE
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pseuAprog := proc(a, b) A000265(a+b) ; end proc:
A179382 := proc(n) local p, k; p := [1] ; for k from 2 do a := pseuAprog( p[-1], 2*n-1) ; if not a in p then p := [op(p), a] ; else return nops(p) ; end if; end do: end proc:
seq(A179382(n), n=1..80) ;
# R. J. Mathar, Jul 13 2010
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PROG
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(PARI) oddres(n)=n>>valuation(n, 2)
a(n)=my(d=2*n-1, k=1, t=1); while((t=oddres(t+d))>1, k++); k
\\ Charles R Greathouse IV, May 15 2013
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CROSSREFS
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Cf. A000265, A001122.
Sequence in context: A184250 A137655 A167595 * A161169 A058202 A217036
Adjacent sequences: A179379 A179380 A179381 * A179383 A179384 A179385
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KEYWORD
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nonn
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AUTHOR
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Vladimir Shevelev, Jul 12 2010
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EXTENSIONS
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Corrected and extended by R. J. Mathar, Jul 13 2010
Removed duplicated database lines - R. J. Mathar, Jul 23 2010
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STATUS
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approved
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