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Search: id:A047778
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| A047778 |
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Concatenation of first n numbers in binary. |
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+0
19
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| 1, 6, 27, 220, 1765, 14126, 113015, 1808248, 28931977, 462911642, 7406586283, 118505380540, 1896086088653, 30337377418462, 485398038695407, 15532737238253040, 497047591624097297, 15905522931971113522
(list; graph; listen)
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OFFSET
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1,2
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FORMULA
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a(n) =a(n-1)*2^(1+floor[log2(n)])+n - Henry Bottomley (se16(AT)btinternet.com), Jan 12 2001
a(n) = 4C / 2^frac(log_2(n)) * n^{n+1} / r(frac(log_2(n)))^n + O(1), where r(x) = 2^{x - 1 + 2^{1-x}}; frac is the fractional part function frac(x) = x - floor(x); and C is the binary Champernowne constant (A066716). (In fact, a(n) is the floor of this expression; the error term is between 1/2 and 1.) r(x) takes on values between e*log(2) and 2 for x in the range 0 to 1. It follows using Stirling's approximation that the radius of convergence for the e.g.f. is log 2. - Frank Adams-Watters (FrankTAW(AT)Netscape.net), Sep 07 2006
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EXAMPLE
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a(4) = 1 10 11 100 = 220
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CROSSREFS
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Cf. A001855 (bit counts, offset by 1), A061168, A066716, A007908.
Adjacent sequences: A047775 A047776 A047777 this_sequence A047779 A047780 A047781
Sequence in context: A117336 A092854 A060977 this_sequence A048436 A006174 A064810
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KEYWORD
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easy,nonn,base,nice
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AUTHOR
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Aaron Gulliver (gulliver(AT)elec.canterbury.ac.nz)
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EXTENSIONS
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More terms from Patrick De Geest (pdg(AT)worldofnumbers.com), May 15 1999.
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