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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
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 A362489
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 March 29 02:23 EDT 2024. Contains 371264 sequences. (Running on oeis4.)