A231670 a(n) = Sum_{i=0..n} digsum_5(i)^3, where digsum_5(i) = A053824(i).

0, 1, 9, 36, 100, 101, 109, 136, 200, 325, 333, 360, 424, 549, 765, 792, 856, 981, 1197, 1540, 1604, 1729, 1945, 2288, 2800, 2801, 2809, 2836, 2900, 3025, 3033, 3060, 3124, 3249, 3465, 3492, 3556, 3681, 3897, 4240, 4304, 4429, 4645, 4988, 5500, 5625, 5841, 6184, 6696, 7425, 7433, 7460, 7524, 7649, 7865, 7892, 7956, 8081, 8297, 8640, 8704, 8829, 9045, 9388, 9900, 10025

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.

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..1000

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.

Mathematica

Accumulate[f[n_]:=n - 4 Sum[Floor[n/5^k], {k, n}]; Array[f, 100, 0]^3] (* Vincenzo Librandi, Sep 04 2016 *)

Crossrefs

Cf. A053824, A231668, A231669, A231671.

Sequence in context: A085630 A133226 A027602 * A134537 A066647 A187607

Adjacent sequences: A231667 A231668 A231669 * A231671 A231672 A231673

Keyword

nonn,base

Author

N. J. A. Sloane, Nov 13 2013

Status

approved