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A231684
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a(n) = Sum_{i=0..n} digsum_9(i), where digsum_9(i) = A053830(i).
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5
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0, 1, 3, 6, 10, 15, 21, 28, 36, 37, 39, 42, 46, 51, 57, 64, 72, 81, 83, 86, 90, 95, 101, 108, 116, 125, 135, 138, 142, 147, 153, 160, 168, 177, 187, 198, 202, 207, 213, 220, 228, 237, 247, 258, 270, 275, 281, 288, 296, 305, 315, 326, 338, 351, 357, 364, 372, 381, 391, 402, 414, 427, 441, 448, 456, 465, 475, 486, 498, 511, 525, 540, 548, 557, 567, 578, 590, 603, 617, 632
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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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MATHEMATICA
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a[n_] := Plus @@ IntegerDigits[n, 9]; Accumulate @ Array[a, 80, 0] (* Amiram Eldar, Dec 09 2021 *)
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PROG
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(PARI) a(n) = sum(i=0, n, sumdigits(i, 9)); \\ Michel Marcus, Sep 20 2017
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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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