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 A054893 a(n) = floor(n/4) + floor(n/16) + floor(n/64) + floor(n/256) + .... 5
 0, 0, 0, 0, 1, 1, 1, 1, 2, 2, 2, 2, 3, 3, 3, 3, 5, 5, 5, 5, 6, 6, 6, 6, 7, 7, 7, 7, 8, 8, 8, 8, 10, 10, 10, 10, 11, 11, 11, 11, 12, 12, 12, 12, 13, 13, 13, 13, 15, 15, 15, 15, 16, 16, 16, 16, 17, 17, 17, 17, 18, 18, 18, 18, 21, 21, 21, 21, 22, 22, 22, 22, 23, 23, 23, 23, 24, 24, 24, 24 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,9 COMMENTS Different from highest power of 4 dividing n! (see A090616). LINKS Hieronymus Fischer, Table of n, a(n) for n = 0..10000 FORMULA a(n) = (n-A053737(n))/3. From Hieronymus Fischer, Sep 15 2007: (Start) Recurrence: a(n) = floor(n/4) + a(floor(n/4)); a(4*n) = n + a(n); a(n*4^m) = n*(4^m-1)/3 + a(n). a(k*4^m) = k*(4^m-1)/3, for 0<=k<4, m>=0. Asymptotic behavior: a(n) = n/3 + O(log(n)), a(n+1) - a(n) = O(log(n)); this follows from the inequalities below. a(n) <= (n-1)/3; equality holds true for powers of 4. a(n) >= (n-3)/3 - floor(log_4(n)); equality holds true for n=4^m-1, m>0. lim inf (n/3-a(n))=1/3, for n-->oo. lim sup (n/3 - log_4(n) - a(n)) = 0, for n-->oo. lim sup (a(n+1) - a(n) - log_4(n)) = 0, for n-->oo. G.f.: g(x) = sum{k>0, x^(4^k)/(1-x^(4^k))}/(1-x). (End) Partial sums of A235127. - R. J. Mathar, Jul 08 2021 EXAMPLE a(100)=32. a(10^3)=330. a(10^4)=3331. a(10^5)=33330. a(10^6)=333330. a(10^7)=3333329. a(10^8)=33333328. a(10^9)=333333326. MATHEMATICA Table[t = 0; p = 4; While[s = Floor[n/p]; t = t + s; s > 0, p *= 4]; t, {n, 0, 100} ] Table[Total[Floor/@(n/NestList[4#&, 4, 6])], {n, 0, 80}] (* Harvey P. Dale, Jun 12 2022 *) CROSSREFS Cf. A011371, A054861, A027868, A054899, A067080, A098844, A132028. Sequence in context: A070548 A209628 A132011 * A090617 A053693 A330324 Adjacent sequences: A054890 A054891 A054892 * A054894 A054895 A054896 KEYWORD nonn,changed AUTHOR Henry Bottomley, May 23 2000 EXTENSIONS Edited by Hieronymus Fischer, Sep 15 2007 Examples added by Hieronymus Fischer, Jun 06 2012 STATUS approved

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Last modified November 30 02:32 EST 2022. Contains 358431 sequences. (Running on oeis4.)