A231681 a(n) = Sum_{i=0..n} digsum_8(i)^2, where digsum_8(i) = A053829(i).

0, 1, 5, 14, 30, 55, 91, 140, 141, 145, 154, 170, 195, 231, 280, 344, 348, 357, 373, 398, 434, 483, 547, 628, 637, 653, 678, 714, 763, 827, 908, 1008, 1024, 1049, 1085, 1134, 1198, 1279, 1379, 1500, 1525, 1561, 1610, 1674, 1755, 1855, 1976, 2120, 2156, 2205, 2269, 2350, 2450, 2571, 2715, 2884, 2933, 2997, 3078, 3178, 3299, 3443, 3612, 3808, 3809, 3813, 3822, 3838, 3863

Offset

0,3

Links

Table of n, a(n) for n=0..68.

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

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

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

J.-L. Mauclaire, 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.

Prog

(PARI) a(n) = sum(i=0, n, sumdigits(i, 8)^2); \\ Michel Marcus, Sep 20 2017

Crossrefs

Cf. A053829, A231680, A231682, A231683.

Sequence in context: A211653 A096893 A231677 * A231685 A074784 A109678

Adjacent sequences: A231678 A231679 A231680 * A231682 A231683 A231684

Keyword

nonn,base

Author

N. J. A. Sloane, Nov 13 2013

Status

approved