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Search: id:A054900
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| A054900 |
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floor[n/16] + floor[n/256] + floor[n/4096] + floor[n/65536] + .... |
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+0
2
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| 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 6, 6, 6, 6, 6, 6, 6, 6, 6
(list; graph; listen)
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OFFSET
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0,33
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FORMULA
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a(n)=(n-A053836(n))/15
Recurrence: a(n)=floor(n/16)+a(floor(n/16)); a(16*n)=n+a(n); a(n*16^m)=n*(16^m-1)/15+a(n). - Hieronymus Fischer (Hieronymus.Fischer(AT)gmx.de), Aug 14 2007
a(k*16^m)=k*(16^m-1)/15, for 0<=k<16, m>=0. - Hieronymus Fischer (Hieronymus.Fischer(AT)gmx.de), Aug 14 2007
Asymptotic behavior: a(n)=n/15+O(log(n)), a(n+1)-a(n)=O(log(n)); this follows from the inequalities below. - Hieronymus Fischer (Hieronymus.Fischer(AT)gmx.de), Aug 14 2007
a(n)<=(n-1)/15; equality holds for powers of 16. - Hieronymus Fischer (Hieronymus.Fischer(AT)gmx.de), Aug 14 2007
a(n)>=(n-15)/15-floor(log_16(n)); equality holds for n=16^m-1, m>0. - Hieronymus Fischer (Hieronymus.Fischer(AT)gmx.de), Aug 14 2007
lim inf (n/15-a(n))=1/15, for n-->oo. - Hieronymus Fischer (Hieronymus.Fischer(AT)gmx.de), Aug 14 2007
lim sup (n/15-log_16(n)-a(n))=0, for n-->oo. - Hieronymus Fischer (Hieronymus.Fischer(AT)gmx.de), Aug 14 2007
lim sup (a(n+1)-a(n)-log_16(n))=0, for n-->oo. - Hieronymus Fischer (Hieronymus.Fischer(AT)gmx.de), Aug 14 2007
G.f.: g(x)=sum{k>0, x^(16^k)/(1-x^(16^k))}/(1-x). - Hieronymus Fischer (Hieronymus.Fischer(AT)gmx.de), Aug 14 2007
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CROSSREFS
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Cf. A011371 and A054861 for analogues involving powers of 2 and 3.
Cf. A054897, A054899, A067080, A098844, A132032.
Sequence in context: A121900 A056811 A097430 this_sequence A046042 A071841 A097876
Adjacent sequences: A054897 A054898 A054899 this_sequence A054901 A054902 A054903
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KEYWORD
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nonn
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AUTHOR
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Henry Bottomley (se16(AT)btinternet.com), May 23 2000
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