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Search: id:A135124
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| A135124 |
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Numbers such that the digital sums in base 2, base 4 and base 8 are all equal. |
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+0
1
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| 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; listen)
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OFFSET
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1,2
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COMMENT
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Written as base 64 numbers the sequence is 1,10,11,100,101,110,111,1000,1001, ... (cf. A007088)
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FORMULA
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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))}.
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EXAMPLE
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a(7)=4161, since ds_2(4161 )=ds_4(4161 )=ds_8(4161 ), where ds_x=digital sum base x.
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CROSSREFS
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Cf. A007953, A054899, A131451, A133620, A133900, A134599, A135100, A135110, A135120, A037308.
Sequence in context: A073327 A123994 A151984 this_sequence A070931 A095533 A044864
Adjacent sequences: A135121 A135122 A135123 this_sequence A135125 A135126 A135127
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KEYWORD
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nonn,base
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AUTHOR
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Hieronymus Fischer (Hieronymus.Fischer(AT)gmx.de), Dec 31 2007, Dec 31 2008
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EXTENSIONS
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Edited by N. J. A. Sloane (njas(AT)research.att.com), Jan 17 2009
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