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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 T. D. Noe, Table of n, a(n) for n = 0..10000 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 Adjacent sequences: A086339 A086340 A086341 * A086343 A086344 A086345 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.)