A382278 a(n) = least integer m >= 2 such that n is a sum of the form Sum_{k>=0} floor(h/m^k) for some integer h >= 1.

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

Offset: 1

Author

Clark Kimberling, Mar 21 2025

Keywords

• nonn

Comments

Let R denote the rectangular array in which row n gives the positions of n+1 in the sequence. Corner of R:

1 3 4 7 8 10 11 15

2 5 6 9 13 14 17 21

12 24 29 33 37 43 52 60

20 51 77 83 226 253 275 306

141 254 285 403 510 541 572 765

(row 1 of R) = A005187(n) for n >= 1.

Examples

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

Crossrefs

Cf. A005187, A381897, A382324.

Programs

Mathematica

testM[n_, m_] := With[{hMin = Floor[(n (m - 1) + m)/m], hMax = 2 n m},
   AnyTrue[Range[hMin, hMax], Total[IntegerDigits[#, m]] == m # - n (m - 1) &]];
a[n_] := SelectFirst[Range[2, n + 1], testM[n, #] &]
t = Map[a, Range[100]]
(* Peter J. C. Moses, Mar 20 2025 *)