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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.

%I A382278 #15 Mar 31 2025 21:21:04
%S A382278 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,
%T A382278 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,
%U A382278 4,2,2,3,2,2,3,3,5,2,2,3,2,2,5,3,2,2
%N 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.
%C A382278 Let R denote the rectangular array in which row n gives the positions of n+1 in the sequence. Corner of R:
%C A382278     1    3    4    7    8   10   11   15
%C A382278     2    5    6    9   13   14   17   21
%C A382278    12   24   29   33   37   43   52   60
%C A382278    20   51   77   83  226  253  275  306
%C A382278   141  254  285  403  510  541  572  765
%C A382278 (row 1 of R) = A005187(n) for n >= 1.
%e A382278 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.
%t A382278 testM[n_, m_] := With[{hMin = Floor[(n (m - 1) + m)/m], hMax = 2 n m},
%t A382278    AnyTrue[Range[hMin, hMax], Total[IntegerDigits[#, m]] == m # - n (m - 1) &]];
%t A382278 a[n_] := SelectFirst[Range[2, n + 1], testM[n, #] &]
%t A382278 t = Map[a, Range[100]]
%t A382278 (* _Peter J. C. Moses_, Mar 20 2025 *)
%Y A382278 Cf. A005187, A381897, A382324.
%K A382278 nonn
%O A382278 1,1
%A A382278 _Clark Kimberling_, Mar 21 2025