A231680 a(n) = Sum_{i=0..n} digsum_8(i), where digsum_8(i) = A053829(i).

0, 1, 3, 6, 10, 15, 21, 28, 29, 31, 34, 38, 43, 49, 56, 64, 66, 69, 73, 78, 84, 91, 99, 108, 111, 115, 120, 126, 133, 141, 150, 160, 164, 169, 175, 182, 190, 199, 209, 220, 225, 231, 238, 246, 255, 265, 276, 288, 294, 301, 309, 318, 328, 339, 351, 364, 371, 379, 388, 398, 409, 421, 434, 448, 449, 451, 454, 458, 463, 469, 476, 484, 486, 489, 493, 498, 504, 511, 519, 528

Offset

0,3

References

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

Links

Amiram Eldar, 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.

Formula

a(n) ~ 7*n*log(n)/(6*log(2)). - Amiram Eldar, Dec 09 2021

Mathematica

a[n_] := Plus @@ IntegerDigits[n, 8]; Accumulate @ Array[a, 80, 0] (* Amiram Eldar, Dec 09 2021 *)

Prog

(PARI) a(n) = sum(i=0, n, sumdigits(i, 8)); \\ Michel Marcus, Sep 20 2017

Crossrefs

Cf. A053829, A231681, A231682, A231683.

Sequence in context: A371473 A130486 A054636 * A124158 A161208 A109444

Adjacent sequences: A231677 A231678 A231679 * A231681 A231682 A231683

Keyword

nonn,base

Author

N. J. A. Sloane, Nov 13 2013

Status

approved