A231673 a(n) = Sum_{i=0..n} digsum_6(i)^2, where digsum_6(i) = A053827(i).

0, 1, 5, 14, 30, 55, 56, 60, 69, 85, 110, 146, 150, 159, 175, 200, 236, 285, 294, 310, 335, 371, 420, 484, 500, 525, 561, 610, 674, 755, 780, 816, 865, 929, 1010, 1110, 1111, 1115, 1124, 1140, 1165, 1201, 1205, 1214, 1230, 1255, 1291, 1340, 1349, 1365, 1390, 1426, 1475, 1539, 1555, 1580, 1616, 1665, 1729, 1810, 1835, 1871, 1920, 1984, 2065, 2165, 2201, 2250, 2314, 2395

Offset

0,3

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.

Mathematica

Accumulate[f[n_]:=n - 5 Sum[Floor[n/6^k], {k, n}]; Array[f, 100, 0]^2] (* Vincenzo Librandi, Sep 04 2016 *)

Crossrefs

Cf. A053827, A231672, A231674, A231675.

Sequence in context: A049791 A053461 A136135 * A211653 A096893 A231677

Adjacent sequences: A231670 A231671 A231672 * A231674 A231675 A231676

Keyword

nonn,base

Author

N. J. A. Sloane, Nov 13 2013

Status

approved