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A094345
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Sum of all digits in ternary expansions of 0, ..., n.
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5
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0, 1, 3, 4, 6, 9, 11, 14, 18, 19, 21, 24, 26, 29, 33, 36, 40, 45, 47, 50, 54, 57, 61, 66, 70, 75, 81, 82, 84, 87, 89, 92, 96, 99, 103, 108, 110, 113, 117, 120, 124, 129, 133, 138, 144, 147, 151, 156, 160, 165, 171, 176, 182, 189, 191, 194, 198, 201, 205, 210, 214, 219
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OFFSET
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0,3
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REFERENCES
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Jean-Paul Allouche and Jeffrey Shallit, Automatic sequences, Cambridge University Press, 2003, p. 94.
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LINKS
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P. J. Grabner, P. Kirschenhofer, H. Prodinger and R. F. Tichy, On the moments of the sum-of-digits function, PDF, Applications of Fibonacci numbers, Vol. 5 (St. Andrews, 1992), pp. 263-271, Kluwer Acad. Publ., Dordrecht, 1993.
J.-L. Mauclaire and Leo Murata, On q-additive functions. I, Proc. Japan Acad. Ser. A Math. Sci., Vol. 59, No. 6 (1983), pp. 274-276.
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FORMULA
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Asymptotically: a(n) = n*log(n)/log(3) + n*F(log(n)/log(3)) where F is a continuous function of period 1 nowhere differentiable (see Allouche & Shallit book).
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MATHEMATICA
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a[n_] := Plus @@ IntegerDigits[n, 3]; Accumulate @ Array[a, 60, 0] (* Amiram Eldar, Dec 09 2021 *)
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PROG
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(PARI) s(k, n)=n-(k-1)*sum(m=1, n, valuation(m, k));
a(n)=sum(i=0, n, s(3, i))
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CROSSREFS
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KEYWORD
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nonn,base
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AUTHOR
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STATUS
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approved
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