A231504 a(n) = Sum_{i=0..n} digsum_3(i)^3, where digsum_3(i) = A053735(i).

0, 1, 9, 10, 18, 45, 53, 80, 144, 145, 153, 180, 188, 215, 279, 306, 370, 495, 503, 530, 594, 621, 685, 810, 874, 999, 1215, 1216, 1224, 1251, 1259, 1286, 1350, 1377, 1441, 1566, 1574, 1601, 1665, 1692, 1756, 1881, 1945, 2070, 2286, 2313, 2377, 2502, 2566, 2691, 2907, 3032, 3248, 3591, 3599, 3626, 3690, 3717, 3781, 3906, 3970, 4095, 4311, 4338, 4402, 4527, 4591, 4716

Offset

0,3

Links

Amiram Eldar, Table of n, a(n) for n = 0..10000

Jean Coquet, Power sums of digital sums, J. Number Theory, Vol. 22, No. 2 (1986), pp. 161-176.

P. J. Grabner, P. Kirschenhofer, H. Prodinger and R. F. Tichy, On the moments of the sum-of-digits function, PDF, Applications of Fibonacci numbers, Vol. 5 (St. Andrews, 1992), Kluwer Acad. Publ., Dordrecht, 1993, pp. 263-271.

J.-L. Mauclaire and Leo Murata, On q-additive functions. I, Proc. Japan Acad. Ser. A Math. Sci., Vol. 59, No. 6 (1983), pp. 274-276.

J.-L. Mauclaire and Leo Murata, On q-additive functions. II, Proc. Japan Acad. Ser. A Math. Sci., Vol. 59, No. 9 (1983), pp. 441-444.

J. R. Trollope, An explicit expression for binary digital sums, Math. Mag., Vol. 41, No. 1 (1968), pp. 21-25.

Mathematica

Accumulate @ Array[(Plus @@ IntegerDigits[#, 3])^3 &, 70, 0] (* Amiram Eldar, Jan 20 2022 *)

Prog

(PARI) a(n) = sum(i=0, n, sumdigits(i, 3)^3); \\ Michel Marcus, Sep 20 2017

Crossrefs

Cf. A053735, A094345, A231503, A231505.

Sequence in context: A110939 A260042 A141640 * A298979 A299969 A050551

Adjacent sequences: A231501 A231502 A231503 * A231505 A231506 A231507

Keyword

nonn,base

Author

N. J. A. Sloane, Nov 13 2013

Status

approved