A231676 - OEIS

%I #24 Dec 10 2021 13:24:54

%S 0,1,3,6,10,15,21,22,24,27,31,36,42,49,51,54,58,63,69,76,84,87,91,96,

%T 102,109,117,126,130,135,141,148,156,165,175,180,186,193,201,210,220,

%U 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

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

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

%H Indranil Ghosh, <a href="/A231676/b231676.txt">Table of n, a(n) for n = 0..10000</a>

%H Jean Coquet, <a href="https://doi.org/10.1016/0022-314X(86)90067-3">Power sums of digital sums</a>, J. Number Theory, Vol. 22, No. 2 (1986), pp. 161-176.

%H P. J. Grabner, P. Kirschenhofer, H. Prodinger and R. F. Tichy, <a href="http://math.sun.ac.za/~hproding/abstract/abs_80.htm">On the moments of the sum-of-digits function</a>, <a href="http://math.sun.ac.za/~hproding/pdffiles/st_andrews.pdf">PDF</a>, Applications of Fibonacci numbers, Vol. 5 (St. Andrews, 1992), pp. 263-271, Kluwer Acad. Publ., Dordrecht, 1993.

%H Hsien-Kuei Hwang, Svante Janson and Tsung-Hsi Tsai, <a href="https://doi.org/10.1145/3127585">Exact and Asymptotic Solutions of a Divide-and-Conquer Recurrence Dividing at Half: Theory and Applications</a>, ACM Transactions on Algorithms, Vol. 13, No. 4 (2017), Article #47; <a href="https://www.researchgate.net/profile/Hsien-Kuei-Hwang/publication/320642171_Exact_and_Asymptotic_Solutions_of_a_Divide-and-Conquer_Recurrence_Dividing_at_Half_Theory_and_Applications/links/59f9a5be0f7e9b553ec0eaad">ResearchGate link</a>; <a href="http://140.109.74.92/hk/wp-content/files/2016/12/aat-hhrr-1.pdf">preprint</a>, 2016.

%H J.-L. Mauclaire and Leo Murata, <a href="https://dx.doi.org/10.3792/pjaa.59.274">On q-additive functions. I</a>, Proc. Japan Acad. Ser. A Math. Sci., Vol. 59, No. 6 (1983), pp. 274-276.

%H J.-L. Mauclaire and Leo Murata, <a href="https://dx.doi.org/10.3792/pjaa.59.441">On q-additive functions. II</a>, Proc. Japan Acad. Ser. A Math. Sci., Vol. 59, No. 9 (1983), pp. 441-444.

%H J. R. Trollope, <a href="http://www.jstor.org/stable/2687954">An explicit expression for binary digital sums</a>, Math. Mag., Vol. 41, No. 1 (1968), pp. 21-25.

%F a(n) ~ 3*n*log(n)/log(7). - _Amiram Eldar_, Dec 09 2021

%t Accumulate[Table[Total[IntegerDigits[n,7]],{n,0,80}]] (* _Harvey P. Dale_, Aug 28 2021 *)

%o (PARI) a(n) = sum(i=0, n, sumdigits(i, 7)); \\ _Michel Marcus_, Dec 09 2021

%Y Cf. A053828, A231677, A231678, A231679.

%K nonn,base

%O 0,3

%A _N. J. A. Sloane_, Nov 13 2013