A231505 a(n) = Sum_{i=0..n} digsum_3(i)^4, where digsum_3(i) = A053735(i).

0, 1, 17, 18, 34, 115, 131, 212, 468, 469, 485, 566, 582, 663, 919, 1000, 1256, 1881, 1897, 1978, 2234, 2315, 2571, 3196, 3452, 4077, 5373, 5374, 5390, 5471, 5487, 5568, 5824, 5905, 6161, 6786, 6802, 6883, 7139, 7220, 7476, 8101, 8357, 8982, 10278, 10359, 10615, 11240, 11496, 12121, 13417, 14042, 15338, 17739, 17755, 17836, 18092, 18173, 18429, 19054, 19310, 19935, 21231

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])^4 &, 60, 0] (* Amiram Eldar, Jan 20 2022 *)

Prog

(PARI) a(n) = sum(i=0, n, sumdigits(i, 3)^4); \\ Michel Marcus, Sep 20 2017

Crossrefs

Cf. A053735, A094345, A231503, A231504.

Sequence in context: A111054 A242975 A155561 * A022107 A041584 A041586

Adjacent sequences: A231502 A231503 A231504 * A231506 A231507 A231508

Keyword

nonn,base

Author

N. J. A. Sloane, Nov 13 2013

Status

approved