A231671 a(n) = Sum_{i=0..n} digsum_5(i)^4, where digsum_5(i) = A053824(i).

0, 1, 17, 98, 354, 355, 371, 452, 708, 1333, 1349, 1430, 1686, 2311, 3607, 3688, 3944, 4569, 5865, 8266, 8522, 9147, 10443, 12844, 16940, 16941, 16957, 17038, 17294, 17919, 17935, 18016, 18272, 18897, 20193, 20274, 20530, 21155, 22451, 24852, 25108, 25733, 27029, 29430, 33526, 34151, 35447, 37848, 41944, 48505, 48521, 48602, 48858, 49483, 50779, 50860, 51116, 51741

Offset: 0

Author

N. J. A. Sloane, Nov 13 2013

Keywords

• nonn
• base

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.

Crossrefs

Cf. A053824, A231668, A231669, A231670.

Programs

Mathematica

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