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A231668 a(n) = Sum_{i=0..n} digsum_5(i), where digsum_5(i) = A053824(i). 4
0, 1, 3, 6, 10, 11, 13, 16, 20, 25, 27, 30, 34, 39, 45, 48, 52, 57, 63, 70, 74, 79, 85, 92, 100, 101, 103, 106, 110, 115, 117, 120, 124, 129, 135, 138, 142, 147, 153, 160, 164, 169, 175, 182, 190, 195, 201, 208, 216, 225, 227, 230, 234, 239, 245, 248, 252, 257, 263, 270, 274, 279, 285, 292, 300, 305, 311, 318, 326, 335, 341, 348, 356, 365, 375, 378, 382, 387, 393, 400 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

REFERENCES

Hsien-Kuei Hwang, S Janson, TH Tsai, Exact and asymptotic solutions of the recurrence f(n) = f(floor(n/2)) + f(ceiling(n/2)) + g(n): theory and applications, Preprint, 2016; http://140.109.74.92/hk/wp-content/files/2016/12/aat-hhrr-1.pdf. Also Exact and Asymptotic Solutions of a Divide-and-Conquer Recurrence Dividing at Half: Theory and Applications, ACM Transactions on Algorithms, 13:4 (2017), #47; DOI: 10.1145/3127585

LINKS

Table of n, a(n) for n=0..79.

Jean Coquet, Power sums of digital sums, J. Number Theory 22 (1986), no. 2, 161-176.

P. J. Grabner, P. Kirschenhofer, H. Prodinger, R. F. Tichy, On the moments of the sum-of-digits function, PDF, Applications of Fibonacci numbers, Vol. 5 (St. Andrews, 1992), 263-271, Kluwer Acad. Publ., Dordrecht, 1993.

J.-L. Mauclaire, Leo Murata, On q-additive functions. I, Proc. Japan Acad. Ser. A Math. Sci. 59 (1983), no. 6, 274-276.

J.-L. Mauclaire, Leo Murata, On q-additive functions. II, Proc. Japan Acad. Ser. A Math. Sci. 59 (1983), no. 9, 441-444.

J. R. Trollope, An explicit expression for binary digital sums, Math. Mag. 41 1968 21-25.

PROG

(PARI) a(n) = sum(i=0, n, sumdigits(i, 5)); \\ Michel Marcus, Sep 20 2017

CROSSREFS

Cf. A053824, A231669, A231670, A231671.

Sequence in context: A290541 A043321 A241858 * A123053 A221129 A138289

Adjacent sequences:  A231665 A231666 A231667 * A231669 A231670 A231671

KEYWORD

nonn,base

AUTHOR

N. J. A. Sloane, Nov 13 2013

STATUS

approved

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Last modified December 16 04:19 EST 2018. Contains 318158 sequences. (Running on oeis4.)