A216789 Table read by antidiagonals: T(n,k) is the digital sum of k in base n displayed in decimal.

0, 0, 1, 0, 1, 1, 0, 1, 2, 2, 0, 1, 2, 1, 1, 0, 1, 2, 3, 2, 2, 0, 1, 2, 3, 1, 3, 2, 0, 1, 2, 3, 4, 2, 2, 3, 0, 1, 2, 3, 4, 1, 3, 3, 1, 0, 1, 2, 3, 4, 5, 2, 4, 4, 2, 0, 1, 2, 3, 4, 5, 1, 3, 2, 1, 2, 0, 1, 2, 3, 4, 5, 6, 2, 4, 3, 2, 3

Offset

2,9

Comments

T(n,k) is the least number of powers of n that add up to k. - Mohammed Yaseen, Nov 12 2022

Links

Robert Israel, Table of n, a(n) for n = 2..10012 (indices corrected to start at 2 by Sidney Cadot, Jan 07 2023)

K. Atanassov, On Some of Smarandache's Problems

Eric Weisstein's World of Mathematics, Digit Sum

Wikipedia, Digit sum

Example

A000120   0, 1, 1, 2, 1, 2, 2, 3, 1, 2,  2,  3,  2,  3,  3,  4, 1, 2, 2
A053735   0, 1, 2, 1, 2, 3, 2, 3, 4, 1,  2,  3,  2,  3,  4,  3, 4, 5, 2
A053737   0, 1, 2, 3, 1, 2, 3, 4, 2, 3,  4,  5,  3,  4,  5,  6, 1, 2, 3
A053824   0, 1, 2, 3, 4, 1, 2, 3, 4, 5,  2,  3,  4,  5,  6,  3, 4, 5, 6
A053827   0, 1, 2, 3, 4, 5, 1, 2, 3, 4,  5,  6,  2,  3,  4,  5, 6, 7, 3
A053828   0, 1, 2, 3, 4, 5, 6, 1, 2, 3,  4,  5,  6,  7,  2,  3, 4, 5, 6
A053829   0, 1, 2, 3, 4, 5, 6, 7, 1, 2,  3,  4,  5,  6,  7,  8, 2, 3, 4
A053830   0, 1, 2, 3, 4, 5, 6, 7, 8, 1,  2,  3,  4,  5,  6,  7, 8, 9, 2
A007953   0, 1, 2, 3, 4, 5, 6, 7, 8, 9,  1,  2,  3,  4,  5,  6, 7, 8, 9
A053831   0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10,  1,  2,  3,  4,  5, 6, 7, 8
A053832   0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11,  1,  2,  3,  4, 5, 6, 7
A053833   0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12,  1,  2,  3, 4, 5, 6
A053834   0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13,  1,  2, 3, 4, 5
A053835   0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14,  1, 2, 3, 4
A053836   0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 1, 2, 3

Maple

[seq(seq(convert(convert(n-b, base, b), `+`), b=n..2, -1), n=1..15)]; # Robert Israel, Aug 02 2020

Mathematica

DigitSum[n_, b_: 10] := Total[IntegerDigits[n, b]]; Table[ DigitSum[n - b, b], {n, 2, 13}, {b, n, 2, -1}] // Flatten

Crossrefs

Cf. A000120, A053735, A053737, A053824, A053827, A053828, A053829, A053830, A007953, A053831, A053832, A053833, A053834, A053835, A053836.

Sequence in context: A146093 A091269 A287455 * A097951 A256171 A058643

Adjacent sequences: A216786 A216787 A216788 * A216790 A216791 A216792

Keyword

base,nonn,tabl

Author

Henry Bottomley & Robert G. Wilson v, Sep 16 2012

Extensions

Name and offset corrected by Mohammed Yaseen, Nov 12 2022

Status

approved