A231675 a(n) = Sum_{i=0..n} digsum_6(i)^4, where digsum_6(i) = A053827(i).

0, 1, 17, 98, 354, 979, 980, 996, 1077, 1333, 1958, 3254, 3270, 3351, 3607, 4232, 5528, 7929, 8010, 8266, 8891, 10187, 12588, 16684, 16940, 17565, 18861, 21262, 25358, 31919, 32544, 33840, 36241, 40337, 46898, 56898, 56899, 56915, 56996, 57252, 57877, 59173, 59189, 59270, 59526, 60151, 61447, 63848, 63929, 64185, 64810, 66106, 68507, 72603, 72859, 73484, 74780, 77181

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 - 5 Sum[Floor[n/6^k], {k, n}]; Array[f, 100, 0]^4] (* Vincenzo Librandi, Sep 04 2016 *)

Crossrefs

Cf. A053827, A231672, A231673, A231674.

Sequence in context: A253707 A160827 A231671 * A231679 A231683 A231687

Adjacent sequences: A231672 A231673 A231674 * A231676 A231677 A231678

Keyword

nonn,base

Author

N. J. A. Sloane, Nov 13 2013

Status

approved