

A179382


a(n) is the smallest period of pseudoarithmetic progression with initial term 1 and difference 2n1.


19



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

1,3


COMMENTS

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 a sequence of the form b, b<+>d, (b<+>d)<+>d,... a pseudoarithmetic progression with the initial term b and the difference d. It is not difficult to prove that every pseudoarithmetic progression is periodic sequence. This sequence lists smallest periods of pseudoarithmetic progressions with initial term 1 and difference 2n1, n=1,2,...
a(n) is the number of distinct odd residues contained in set {1,2,...,2^(2*n2)} modulo 2*n1. Thus 2*n1 is in A001122 iff a(n)=n1.  Vladimir Shevelev, Jul 18 2010


LINKS

Peter J. C. Moses, Table of n, a(n) for n = 1..4096


FORMULA

a(n) = A001222(A292239(n1)).  Antti Karttunen, Oct 04 2017


EXAMPLE

For n=5, we have 1<+>9=5, 5<+>9=7, 7<+>9=1. Thus a(5)=3.


MAPLE

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*n1) ; 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


MATHEMATICA

oddres[n_] := n/2^IntegerExponent[n, 2];
a[n_] := Module[{d = 2n1, k=1, t=1}, While[(t = oddres[t+d])>1, k++]; k];
Array[a, 80] (* JeanFrançois Alcover, Apr 13 2020, translated from PARI *)


PROG

(PARI) oddres(n)=n>>valuation(n, 2)
a(n)=my(d=2*n1, k=1, t=1); while((t=oddres(t+d))>1, k++); k
\\ Charles R Greathouse IV, May 15 2013
(Sage)
def A179382(n):
N, o, s = 2*n1, 1, 0
while True:
o = (N + o) >> valuation(N + o, 2)
s = s + 1
if o == 1: break
return s
print([A179382(n) for n in (1..72)]) # Peter Luschny, Oct 07 2017


CROSSREFS

Cf. A000265, A001122, A179680, A292239.
Sequence in context: A296064 A167595 A328600 * A161169 A239738 A058202
Adjacent sequences: A179379 A179380 A179381 * A179383 A179384 A179385


KEYWORD

nonn


AUTHOR

Vladimir Shevelev, Jul 12 2010


EXTENSIONS

Corrected and extended by R. J. Mathar, Jul 13 2010
Duplicated database lines removed by R. J. Mathar, Jul 23 2010


STATUS

approved



