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 A054900 a(n) = Sum_{j >= 1} floor(n/16^j). 3
 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; refs; listen; history; text; internal format)
 OFFSET 0,33 LINKS G. C. Greubel, Table of n, a(n) for n = 0..10000 FORMULA a(n) = (n - A053836(n))/15. From Hieronymus Fischer, Aug 14 2007: (Start) Recurrence: a(n) = a(floor(n/16)) + floor(n/16). a(16*n) = a(n) + n. a(n*16^m) = a(n) + n*(16^m - 1)/15. a(k*16^m) = k*(16^m - 1)/15, for 0 <= k < 16, m>=0. Asymptotic behavior: a(n) = n/15 + O(log(n)). a(n+1) - a(n) = O(log(n)) (this follows from the inequalities below). a(n) <= (n-1)/15; equality holds for powers of 16. a(n) >= (n-15)/15 - floor(log_16(n)); equality holds for n = 16^m - 1, m > 0. Limits: lim inf (n/15 - a(n)) = 1/15, for n --> oo. lim sup (n/15 - log_16(n) - a(n)) = 0, for n --> oo. lim sup (a(n+1) - a(n) - log_16(n)) = 0, for n --> oo. Series: G.f.: (1/(1-x))*Sum_{k > 0} x^(16^k)/(1-x^(16^k)). (End) MATHEMATICA a[n_, m_]:= If[n==0, 0, a[Floor[n/m], m] +Floor[n/m]]; Table[a[n, 16], {n, 0, 127}] (* G. C. Greubel, Apr 28 2023 *) PROG (Magma) m:=16; function a(n) // a = A054900, m = 16 if n eq 0 then return 0; else return a(Floor(n/m)) + Floor(n/m); end if; end function; [a(n): n in [0..127]]; // G. C. Greubel, Apr 28 2023 (SageMath) m=16 # a = A054900 def a(n): return 0 if (n==0) else a(n//m) + (n//m) [a(n) for n in range(128)] # G. C. Greubel, Apr 28 2023 CROSSREFS Cf. A011371 and A054861 for analogs involving powers of 2 and 3. Cf. A053836, A054897, A054899, A067080, A098844, A132032. Sequence in context: A373095 A056811 A097430 * A046042 A287866 A071841 Adjacent sequences: A054897 A054898 A054899 * A054901 A054902 A054903 KEYWORD nonn AUTHOR Henry Bottomley, May 23 2000 STATUS approved

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Last modified September 11 16:56 EDT 2024. Contains 375836 sequences. (Running on oeis4.)