Search: id:A054897
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%I A054897
%S A054897 0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,3,3,3,3,3,3,3,3,4,4,4,
%T A054897 4,4,4,4,4,5,5,5,5,5,5,5,5,6,6,6,6,6,6,6,6,7,7,7,7,7,7,7,7,9,9,9,9,9,9,
%U A054897 9,9,10,10,10,10,10,10,10,10,11,11,11,11,11,11,11,11,12,12,12,12,12,12
%N A054897 Sum_{k>0} floor(n/8^k).
%C A054897 Different from the highest power of 8 dividing n!.
%F A054897 floor[n/8] + floor[n/64] + floor[n/512] + floor[n/4096] + ....
%F A054897 a(n)=(n-A053829(n))/7
%F A054897 Recurrence: a(n)=floor(n/8)+a(floor(n/8)); a(8*n)=n+a(n); a(n*8^m)=n*(8^m-1)/
               7+a(n). - Hieronymus Fischer (Hieronymus.Fischer(AT)gmx.de), Aug 
               14 2007
%F A054897 a(k*8^m)=k*(8^m-1)/7, for 0<=k<8, m>=0. - Hieronymus Fischer (Hieronymus.Fischer(AT)gmx.de), 
               Aug 14 2007
%F A054897 Asymptotic behavior: a(n)=n/7+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
%F A054897 a(n)<=(n-1)/7; equality holds for powers of 8. - Hieronymus Fischer (Hieronymus.Fischer(AT)gmx.de), 
               Aug 14 2007
%F A054897 a(n)>=(n-7)/7-floor(log_8(n)); equality holds for n=8^m-1, m>0. - Hieronymus 
               Fischer (Hieronymus.Fischer(AT)gmx.de), Aug 14 2007
%F A054897 lim inf (n/7-a(n))=1/7, for n-->oo. - Hieronymus Fischer (Hieronymus.Fischer(AT)gmx.de), 
               Aug 14 2007
%F A054897 lim sup (n/7-log_8(n)-a(n))=0, for n-->oo. - Hieronymus Fischer (Hieronymus.Fischer(AT)gmx.de), 
               Aug 14 2007
%F A054897 lim sup (a(n+1)-a(n)-log_8(n))=0, for n-->oo. - Hieronymus Fischer (Hieronymus.Fischer(AT)gmx.de), 
               Aug 14 2007
%F A054897 G.f.: g(x)=sum{k>0, x^(8^k)/(1-x^(8^k))}/(1-x). - Hieronymus Fischer 
               (Hieronymus.Fischer(AT)gmx.de), Aug 14 2007
%t A054897 Table[t = 0; p = 8; While[s = Floor[n/p]; t = t + s; s > 0, p *= 8]; 
               t, {n, 0, 100} ]
%Y A054897 Cf. A011371 and A054861 for analogues involving powers of 2 and 3.
%Y A054897 Cf. A054899, A067080, A098844, A132032.
%Y A054897 Sequence in context: A132292 A110656 A104407 this_sequence A003108 A111898 
               A072746
%Y A054897 Adjacent sequences: A054894 A054895 A054896 this_sequence A054898 A054899 
               A054900
%K A054897 nonn
%O A054897 0,17
%A A054897 Henry Bottomley (se16(AT)btinternet.com), May 23 2000

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