A216789 - OEIS

%I #24 Jan 08 2023 11:49:43

%S 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,

%T 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,

%U 2,3,4,5,6,2,4,3,2,3

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

%C T(n,k) is the least number of powers of n that add up to k. - _Mohammed Yaseen_, Nov 12 2022

%H Robert Israel, <a href="/A216789/b216789.txt">Table of n, a(n) for n = 2..10012</a> (indices corrected to start at 2 by Sidney Cadot, Jan 07 2023)

%H K. Atanassov, <a href="http://www.gallup.unm.edu/~smarandache/Atanassov-SomeProblems.pdf">On Some of Smarandache's Problems</a>

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/DigitSum.html">Digit Sum</a>

%H Wikipedia, <a href="http://en.wikipedia.org/wiki/Digit_sum">Digit sum</a>

%e A000120   0, 1, 1, 2, 1, 2, 2, 3, 1, 2,  2,  3,  2,  3,  3,  4, 1, 2, 2

%e A053735   0, 1, 2, 1, 2, 3, 2, 3, 4, 1,  2,  3,  2,  3,  4,  3, 4, 5, 2

%e A053737   0, 1, 2, 3, 1, 2, 3, 4, 2, 3,  4,  5,  3,  4,  5,  6, 1, 2, 3

%e A053824   0, 1, 2, 3, 4, 1, 2, 3, 4, 5,  2,  3,  4,  5,  6,  3, 4, 5, 6

%e A053827   0, 1, 2, 3, 4, 5, 1, 2, 3, 4,  5,  6,  2,  3,  4,  5, 6, 7, 3

%e A053828   0, 1, 2, 3, 4, 5, 6, 1, 2, 3,  4,  5,  6,  7,  2,  3, 4, 5, 6

%e A053829   0, 1, 2, 3, 4, 5, 6, 7, 1, 2,  3,  4,  5,  6,  7,  8, 2, 3, 4

%e A053830   0, 1, 2, 3, 4, 5, 6, 7, 8, 1,  2,  3,  4,  5,  6,  7, 8, 9, 2

%e A007953   0, 1, 2, 3, 4, 5, 6, 7, 8, 9,  1,  2,  3,  4,  5,  6, 7, 8, 9

%e A053831   0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10,  1,  2,  3,  4,  5, 6, 7, 8

%e A053832   0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11,  1,  2,  3,  4, 5, 6, 7

%e A053833   0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12,  1,  2,  3, 4, 5, 6

%e A053834   0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13,  1,  2, 3, 4, 5

%e A053835   0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14,  1, 2, 3, 4

%e A053836   0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 1, 2, 3

%p [seq(seq(convert(convert(n-b,base,b),`+`),b=n..2,-1),n=1..15)]; # _Robert Israel_, Aug 02 2020

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

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

%K base,nonn,tabl

%O 2,9

%A _Henry Bottomley_ & _Robert G. Wilson v_, Sep 16 2012

%E Name and offset corrected by _Mohammed Yaseen_, Nov 12 2022