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A231676 a(n) = Sum_{i=0..n} digsum_7(i), where digsum_7(i) = A053828(i). 5
0, 1, 3, 6, 10, 15, 21, 22, 24, 27, 31, 36, 42, 49, 51, 54, 58, 63, 69, 76, 84, 87, 91, 96, 102, 109, 117, 126, 130, 135, 141, 148, 156, 165, 175, 180, 186, 193, 201, 210, 220, 231, 237, 244, 252, 261, 271, 282, 294, 295, 297, 300, 304, 309, 315, 322, 324, 327, 331, 336, 342, 349, 357, 360, 364, 369, 375, 382, 390, 399, 403, 408, 414, 421, 429, 438, 448, 453, 459, 466 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

REFERENCES

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

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

Indranil Ghosh, Table of n, a(n) for n =0..10000

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

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

J.-L. Mauclaire and 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) sd(n) = my(d=digits(n, 7)); vecsum(d);

a(n) = sum(k=0, n, sd(k)); \\ Michel Marcus, Jan 07 2017

CROSSREFS

Cf. A053828, A231677, A231678, A231679.

Sequence in context: A139131 A130485 A115015 * A056150 A310081 A240443

Adjacent sequences:  A231673 A231674 A231675 * A231677 A231678 A231679

KEYWORD

nonn,base

AUTHOR

N. J. A. Sloane, Nov 13 2013

STATUS

approved

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Last modified December 16 04:05 EST 2019. Contains 330013 sequences. (Running on oeis4.)