A231679 a(n) = Sum_{i=0..n} digsum_7(i)^4, where digsum_7(i) = A053828(i).

0, 1, 17, 98, 354, 979, 2275, 2276, 2292, 2373, 2629, 3254, 4550, 6951, 6967, 7048, 7304, 7929, 9225, 11626, 15722, 15803, 16059, 16684, 17980, 20381, 24477, 31038, 31294, 31919, 33215, 35616, 39712, 46273, 56273, 56898, 58194, 60595, 64691, 71252, 81252, 95893, 97189, 99590, 103686, 110247, 120247, 134888, 155624, 155625, 155641, 155722, 155978, 156603, 157899, 160300

Offset

0,3

Links

Harvey P. Dale, Table of n, a(n) for n = 0..1000

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.

Example

a(9): we write 0 though 9 in base 7: 0, 1, 2, ...,6, 10, 11, 12; take sums of those digits: 0, 1, 2, ..., 6, 1, 2, 3; raise them to 4th power: 0, 1, 16, ..., 1296, 1, 16, 81; total is 2373 = a(9). - N. J. A. Sloane, Feb 27 2023

Mathematica

Accumulate[Table[Total[IntegerDigits[n, 7]]^4, {n, 0, 60}]] (* Harvey P. Dale, Feb 28 2023 *)

Prog

(PARI) a(n) = sum(i=0, n, sumdigits(i, 7)^4);

Crossrefs

Cf. A053828, A231676, A231677, A231678.

Sequence in context: A160827 A231671 A231675 * A231683 A231687 A231689

Adjacent sequences: A231676 A231677 A231678 * A231680 A231681 A231682

Keyword

nonn,base

Author

N. J. A. Sloane, Nov 13 2013

Status

approved