A374383 Triangle T(n, k), n > 0, k = 0..n-1, read by rows; T(n, k) is the least base b >= 2 where n and k have different sums of digits.

2, 2, 3, 2, 2, 2, 2, 3, 4, 2, 2, 2, 2, 3, 2, 2, 2, 2, 3, 2, 3, 2, 2, 2, 2, 2, 2, 2, 2, 3, 3, 2, 3, 2, 2, 2, 2, 2, 2, 5, 2, 3, 3, 2, 2, 2, 2, 2, 3, 2, 3, 4, 2, 2, 3, 2, 2, 2, 2, 2, 2, 2, 4, 2, 2, 2, 2, 2, 2, 3, 2, 3, 5, 2, 2, 3, 4, 2, 2, 2, 2, 2, 2, 2, 2, 5, 2, 2, 2, 4, 2

Offset: 1

Author

Rémy Sigrist, Jul 07 2024

Keywords

• nonn
• base
• tabl

Examples

			Triangle T(n, k) begins:
  n   n-th row
  --  ----------------------------------
   1  2
   2  2, 3
   3  2, 2, 2
   4  2, 3, 4, 2
   5  2, 2, 2, 3, 2
   6  2, 2, 2, 3, 2, 3
   7  2, 2, 2, 2, 2, 2, 2
   8  2, 3, 3, 2, 3, 2, 2, 2
   9  2, 2, 2, 5, 2, 3, 3, 2, 2
  10  2, 2, 2, 3, 2, 3, 4, 2, 2, 3
  11  2, 2, 2, 2, 2, 2, 2, 4, 2, 2, 2
  12  2, 2, 2, 3, 2, 3, 5, 2, 2, 3, 4, 2
		

Crossrefs

Cf. A374381.

Programs

Mathematica

T[n_,k_]:=Module[{b=2},While[DigitSum[n,b]==DigitSum[k,b], b++]; b]; Table[T[n,k],{n,13},{k,0,n-1}]//Flatten (* Stefano Spezia, Jul 12 2024 *)

PARI

T(n, k) = { for (b = 2, oo, my (d = sumdigits(n, b) - sumdigits(k, b)); if (d, return (b););); }

Formula

T(n, 0) = 2.

T(n, k) <= n+1.