A231676 a(n) = Sum_{i=0..n} digsum_7(i), where digsum_7(i) = A053828(i).

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

Offset: 0

Author

N. J. A. Sloane, Nov 13 2013

Keywords

• nonn
• base

References

• Jean-Paul Allouche and Jeffrey Shallit, Automatic sequences, Cambridge University Press, 2003, p. 94.

Links

• Indranil Ghosh, Table of n, a(n) for n = 0..10000
• Jean Coquet, Power sums of digital sums, J. Number Theory, Vol. 22, No. 2 (1986), pp. 161-176.
• 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.
• Hsien-Kuei Hwang, Svante Janson and Tsung-Hsi Tsai, Exact and Asymptotic Solutions of a Divide-and-Conquer Recurrence Dividing at Half: Theory and Applications, ACM Transactions on Algorithms, Vol. 13, No. 4 (2017), Article #47; ResearchGate link; preprint, 2016.
• 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.
• J.-L. Mauclaire and Leo Murata, On q-additive functions. II, Proc. Japan Acad. Ser. A Math. Sci., Vol. 59, No. 9 (1983), pp. 441-444.
• J. R. Trollope, An explicit expression for binary digital sums, Math. Mag., Vol. 41, No. 1 (1968), pp. 21-25.

Crossrefs

Cf. A053828, A231677, A231678, A231679.

Programs

Mathematica

Accumulate[Table[Total[IntegerDigits[n,7]],{n,0,80}]] (* Harvey P. Dale, Aug 28 2021 *)

PARI

a(n) = sum(i=0, n, sumdigits(i, 7)); \\ Michel Marcus, Dec 09 2021

Formula

a(n) ~ 3*n*log(n)/log(7). - Amiram Eldar, Dec 09 2021