A231669 - OEIS

%I #7 Sep 20 2017 11:46:36

%S 0,1,5,14,30,31,35,44,60,85,89,98,114,139,175,184,200,225,261,310,326,

%T 351,387,436,500,501,505,514,530,555,559,568,584,609,645,654,670,695,

%U 731,780,796,821,857,906,970,995,1031,1080,1144,1225,1229,1238,1254,1279,1315,1324,1340,1365,1401,1450,1466,1491,1527,1576,1640,1665,1701,1750,1814,1895,1931,1980

%N a(n) = Sum_{i=0..n} digsum_5(i)^2, where digsum_5(i) = A053824(i).

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

%H P. J. Grabner, P. Kirschenhofer, H. Prodinger, 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), 263-271, Kluwer Acad. Publ., Dordrecht, 1993.

%H J.-L. Mauclaire, 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. 59 (1983), no. 6, 274-276.

%H J.-L. Mauclaire, 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. 59 (1983), no. 9, 441-444.

%H J. R. Trollope, <a href="http://www.jstor.org/stable/2687954">An explicit expression for binary digital sums</a>, Math. Mag. 41 1968 21-25.

%o (PARI) a(n) = sum(i=0, n, sumdigits(i, 5)^2); \\ _Michel Marcus_, Sep 20 2017

%Y Cf. A053824, A231668, A231670, A231671.

%K nonn,base

%O 0,3

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