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 A054897 a(n) = Sum_{k>0} floor(n/8^k). 4
 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, 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, 9, 9, 10, 10, 10, 10, 10, 10, 10, 10, 11, 11, 11, 11, 11, 11, 11, 11, 12, 12, 12, 12, 12, 12 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,17 COMMENTS Different from the highest power of 8 dividing n!. LINKS Hieronymus Fischer, Table of n, a(n) for n = 0..10000 FORMULA floor[n/8] + floor[n/64] + floor[n/512] + floor[n/4096] + .... a(n) = (n-A053829(n))/7. From Hieronymus Fischer, Aug 14 2007: (Start) 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). a(k*8^m) = k*(8^m-1)/7, for 0<=k<8, m>=0. Asymptotic behavior: a(n) = n/7 + O(log(n)), a(n+1) - a(n) = O(log(n)); this follows from the inequalities below. a(n) <= (n-1)/7; equality holds for powers of 8. a(n) >= (n-7)/7 - floor(log_8(n)); equality holds for n=8^m-1, m>0. lim inf (n/7 - a(n)) = 1/7, for n-->oo. lim sup (n/7 - log_8(n) - a(n)) = 0, for n-->oo. lim sup (a(n+1) - a(n) - log_8(n)) = 0, for n-->oo. G.f.: g(x) = sum{k>0, x^(8^k)/(1-x^(8^k))}/(1-x). (End) EXAMPLE a(100)=13. a(10^3)=141. a(10^4)=1427. a(10^5)=14284. a(10^6)=142855. a(10^7)=1428569. a(10^8)=14285710. a(10^9)=142857138. MATHEMATICA Table[t = 0; p = 8; While[s = Floor[n/p]; t = t + s; s > 0, p *= 8]; t, {n, 0, 100} ] CROSSREFS Cf. A011371 and A054861 for analogs involving powers of 2 and 3. Cf. A054899, A067080, A098844, A132032. Sequence in context: A132292 A110656 A104407 * A261226 A003108 A279223 Adjacent sequences:  A054894 A054895 A054896 * A054898 A054899 A054900 KEYWORD nonn AUTHOR Henry Bottomley, May 23 2000 EXTENSIONS Examples added by Hieronymus Fischer, Jun 06 2012 STATUS approved

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Last modified August 11 15:12 EDT 2020. Contains 336428 sequences. (Running on oeis4.)