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 A160824 a(1)=1, a(n) = the smallest positive integer such that both a(n) and Sum_{k=1..n} a(k) have the same number of (nonleading) 0's when they are represented in binary. 2
 1, 5, 1, 6, 9, 4, 18, 8, 36, 16, 72, 32, 144, 64, 288, 128, 576, 256, 1152, 512, 2304, 1024, 4608, 2048, 9216, 4096, 18432, 8192, 36864, 16384, 73728, 32768, 147456, 65536, 294912, 131072, 589824, 262144, 1179648, 524288, 2359296, 1048576, 4718592 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS Sum_{k=1..n} a(k) = A160825(n). Consider the related sequence {b(k)}, where b(1) = 1, b(n) = the smallest positive integer such that both b(n) and Sum_{k=1..n} b(k) have the same number of 1's when they are represented in binary. Then b(1) = 1, and b(n) = 2^(n-2), for all n >= 2. (b(n) = A011782(n-1).) LINKS G. C. Greubel, Table of n, a(n) for n = 1..1000 FORMULA a(2n) = 2^(n-1) and a(2n-1) = 9*2^(n-3) for n >= 3 (cf. formula for A160825). - Hagen von Eitzen, Jun 01 2009 G.f.: (-8*x^5 + 7*x^4 - 4*x^3 - x^2 + 5*x + 1)/(-2*x^2 + 1). - Alexander R. Povolotsky, Jun 08 2009 MATHEMATICA CoefficientList[Series[(-8*x^5 + 7*x^4 - 4*x^3 - x^2 + 5*x + 1)/(-2*x^2 + 1), {x, 0, 50}], x] (* G. C. Greubel, Feb 22 2017 *) PROG (PARI) x='x + O('x^50); Vec((-8*x^5 + 7*x^4 - 4*x^3 - x^2 + 5*x + 1)/(-2*x^2 + 1)) \\ G. C. Greubel, Feb 22 2017 CROSSREFS Cf. A160825. Sequence in context: A058651 A164105 A262153 * A193586 A007397 A204203 Adjacent sequences:  A160821 A160822 A160823 * A160825 A160826 A160827 KEYWORD nonn,base AUTHOR Leroy Quet, May 27 2009 EXTENSIONS Extended by Ray Chandler, Jun 15 2009 Edited by N. J. A. Sloane, Jul 31 2009 at the suggestion of R. J. Mathar STATUS approved

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Last modified December 17 00:14 EST 2018. Contains 318191 sequences. (Running on oeis4.)