A231503 a(n) = Sum_{i=0..n} digsum_3(i)^2, where digsum_3(i) = A053735(i).

0, 1, 5, 6, 10, 19, 23, 32, 48, 49, 53, 62, 66, 75, 91, 100, 116, 141, 145, 154, 170, 179, 195, 220, 236, 261, 297, 298, 302, 311, 315, 324, 340, 349, 365, 390, 394, 403, 419, 428, 444, 469, 485, 510, 546, 555, 571, 596, 612, 637, 673, 698, 734, 783, 787, 796, 812, 821, 837, 862, 878, 903, 939, 948, 964, 989, 1005, 1030, 1066, 1091, 1127, 1176, 1192, 1217, 1253, 1278

Offset: 0

Author

N. J. A. Sloane, Nov 13 2013

Keywords

• nonn
• base

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.

Crossrefs

Cf. A053735, A094345, A231504, A231505.

Programs

Mathematica

Accumulate @ (Table[Plus @@ IntegerDigits[n, 3], {n, 0, 75}]^2) (* Amiram Eldar, Jan 20 2022 *)

PARI

a(n) = sum(i=0, n, sumdigits(i, 3)^2); \\ Michel Marcus, Sep 20 2017