

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
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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^(n2), for all n >= 2. (b(n) = A011782(n1).)


LINKS

G. C. Greubel, Table of n, a(n) for n = 1..1000


FORMULA

a(2n) = 2^(n1) and a(2n1) = 9*2^(n3) 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



