A240236 - OEIS

%I #37 Jan 13 2025 17:02:10

%S 1,2,1,1,2,1,2,3,2,1,2,2,3,2,1,3,3,4,3,2,1,1,4,2,4,3,2,1,2,1,3,5,4,3,

%T 2,1,2,2,4,2,5,4,3,2,1,3,3,5,3,6,5,4,3,2,1,2,2,3,4,2,6,5,4,3,2,1,3,3,

%U 4,5,3,7,6,5,4,3,2,1,3,4,5,6,4,2,7,6,5,4,3,2,1

%N Triangle read by rows: sum of digits of n in base k, for 2<=k<=n.

%H Reinhard Zumkeller, <a href="/A240236/b240236.txt">Rows n = 2..100 of triangle, flattened</a>

%F T(n,k) = n - (k - 1) * Sum_{i=1..floor(log_k(n))} floor(n/k^i). - _Ridouane Oudra_, Sep 27 2024

%e Triangle starts:

%e   1

%e   2 1

%e   1 2 1

%e   2 3 2 1

%e   2 2 3 2 1

%e   3 3 4 3 2 1

%t Table[Total[Flatten[IntegerDigits[n,k]]],{n,20},{k,2,n}]//Flatten (* _Harvey P. Dale_, Jan 13 2025 *)

%o (PARI) T(n,k) = local(r=0);if(k<2,-1,while(n>0,r+=n%k;n\=k);r)

%o (Haskell)

%o a240236 n k = a240236_tabl !! (n-1) !! (k-1)

%o a240236_row n = a240236_tabl !! (n-1)

%o a240236_tabl = zipWith (map . flip q)

%o                        [2..] (map tail $ tail a002260_tabl) where

%o    q b n = if n < b then n else q b n' + d where (n', d) = divMod n b

%o -- _Reinhard Zumkeller_, Apr 29 2015

%Y Row sums give A043306.

%Y Cf. A000120, A053735, A053737, A007953.

%Y See A138530 for another version.

%Y  Cf. A002260.

%K nonn,tabl,base,changed

%O 2,2

%A _Franklin T. Adams-Watters_, Apr 02 2014