A382324 a(n) = least integer h >= 1 such that n is a sum of the form Sum_{k>=0} floor(h/m^k) for some integer m >= 2.

1, 2, 2, 3, 4, 5, 4, 5, 7, 6, 7, 10, 9, 10, 8, 9, 12, 10, 11, 17, 15, 12, 13, 19, 14, 15, 19, 20, 23, 21, 16, 17, 26, 18, 19, 26, 29, 20, 21, 27, 22, 23, 33, 30, 31, 24, 25, 33, 26, 27, 42, 40, 28, 29, 38, 30, 31, 40, 41, 47, 42, 43, 32, 33, 50, 34, 35, 47

Offset: 1

Author

Clark Kimberling, Apr 01 2025

Keywords

• nonn

Examples

			a(12) = 10, because 10 is the least h such that 12 is a sum of the form Sum_{k>=0} floor(h/m^k) for some m >= 2; that sum is [10/1] + [10/4], where [ ] = floor.
		

Crossrefs

Cf. A382278.

Programs

Mathematica

findH[n_, m_] := With[{hMin = Floor[(n*(m - 1) + m)/m], hMax = 2*n*m},
   SelectFirst[Range[hMin, hMax], Total[IntegerDigits[#1, m]] == m*#1 - n*(m - 1) &, None]];
aPair[n_] := With[{m = SelectFirst[Range[2, n + 1], findH[n, #1] =!= None &, None]},
If[m === None, None, {m, findH[n, m]}]];
t = ({#1, aPair[#1]} &) /@ Range[100]
Map[Last, Map[Last, t]]
(* Peter J. C. Moses, Mar 20 2025 *)