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A086342 Smallest number of 1's in binary expansion of any positive multiple of n. 6
0, 1, 1, 2, 1, 2, 2, 3, 1, 2, 2, 2, 2, 2, 3, 4, 1, 2, 2, 2, 2, 3, 2, 3, 2, 2, 2, 2, 3, 2, 4, 5, 1, 2, 2, 3, 2, 2, 2, 3, 2, 2, 3, 2, 2, 4, 3, 3, 2, 3, 2, 4, 2, 2, 2, 3, 3, 2, 2, 2, 4, 2, 5, 6, 1, 2, 2, 2, 2, 3, 3, 3, 2, 3, 2, 4, 2, 3, 3, 3, 2, 2, 2, 2, 3, 4, 2, 3, 2, 4, 4, 3, 3, 5, 3, 3, 2, 2, 3, 2, 2, 2, 4, 3, 2 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,4
COMMENTS
If n is a power of 2 then a(n)=1. All other positive n have a(n)>1. a(n)=2 precisely in cases where some multiple of n is a factor of 2^q+1 for some q.
LINKS
Trevor Clokie et al., Computational Aspects of Sturdy and Flimsy Numbers, arxiv preprint arXiv:2002.02731 [cs.DS], February 7 2020.
FORMULA
a(2^k-1) = k. - Thomas Dybdahl Ahle, May 01 2013
EXAMPLE
a(n)=2 for n=53, 59, 61, 67, 81, 97 and 101 because n divides 2^k+1 for k=26, 29, 30, 33, 27, 24 and 50, respectively. - T. D. Noe, Jul 22 2008
PROG
(PARI) a(n)=if(!n, return(0)); n>>=valuation(n, 2); my(o=znorder(Mod(2, n)), v1=Set(powers(Mod(2, n), o)), v=v1, s=1); while(!setsearch(v, Mod(0, n)), v=setbinop((x, y)->x+y, v, v1); s++); s \\ Charles R Greathouse IV, Dec 07 2016
CROSSREFS
Cf. A005360 (flimsy numbers), A125121 (sturdy numbers), A143069 (least multiple).
Sequence in context: A355300 A211097 A354907 * A274036 A194449 A261923
KEYWORD
base,nonn
AUTHOR
Sean A. Irvine, Sep 02 2003
EXTENSIONS
More terms from Robert G. Wilson v, Feb 21 2005
Corrected by T. D. Noe, Jul 22 2008
An incorrect Mathematica program was deleted Aug 01 2008
STATUS
approved

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Last modified February 27 15:42 EST 2024. Contains 370377 sequences. (Running on oeis4.)