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A135124 Numbers such that the digital sums in base 2, base 4 and base 8 are all equal. 0
1, 64, 65, 4096, 4097, 4160, 4161, 262144, 262145, 262208, 262209, 266240, 266241, 266304, 266305, 16777216, 16777217, 16777280, 16777281, 16781312, 16781313, 16781376, 16781377, 17039360, 17039361, 17039424, 17039425, 17043456 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Written as base 64 numbers the sequence is 1,10,11,100,101,110,111,1000,1001, ... (cf. A007088)

LINKS

Table of n, a(n) for n=1..28.

FORMULA

a(n)=(1/2)*sum{0<=k<=floor(log_2(n)), (1-(-1)^floor(n/2^k))*64^k}.

G.f.: g(x)=(1/(1-x))*sum{k>=0, 64^k*x^(2^k)/(1+x^(2^k))}.

EXAMPLE

a(7)=4161, since ds_2(4161 )=ds_4(4161 )=ds_8(4161 ), where ds_x=digital sum base x.

MATHEMATICA

Select[Range[500000], Total[IntegerDigits[#, 2]] == Total[IntegerDigits[#, 4]] == Total[IntegerDigits[#, 8]] &] (* G. C. Greubel, Sep 26 2016 *)

CROSSREFS

Cf. A007953, A054899, A131451, A133620, A133900, A134599, A135100, A135110, A135120, A037308.

Sequence in context: A151984 A194769 A217846 * A223590 A070931 A095533

Adjacent sequences:  A135121 A135122 A135123 * A135125 A135126 A135127

KEYWORD

nonn,base

AUTHOR

Hieronymus Fischer, Dec 31 2007, Dec 31 2008

EXTENSIONS

Edited by N. J. A. Sloane, Jan 17 2009

STATUS

approved

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Last modified April 13 05:48 EDT 2021. Contains 342935 sequences. (Running on oeis4.)