cp's OEIS Frontend

A375968 a(n) is the least number with the same digit average as n.

%I A375968 #12 Sep 08 2024 07:54:41
%S A375968 0,1,2,3,4,5,6,7,8,9,10,1,12,2,14,3,16,4,18,5,1,12,2,14,3,16,4,18,5,
%T A375968 29,12,2,14,3,16,4,18,5,29,6,2,14,3,16,4,18,5,29,6,49,14,3,16,4,18,5,
%U A375968 29,6,49,7,3,16,4,18,5,29,6,49,7,69,16,4,18,5,29,6
%N A375968 a(n) is the least number with the same digit average as n.
%C A375968 The digit average of a number n is its sum of digits divided by its number of digits: A007953(n) / A055642(n).
%H A375968 Rémy Sigrist, <a href="/A375968/b375968.txt">Table of n, a(n) for n = 0..10000</a>
%e A375968 The first terms, alongside the corresponding digit average, are:
%e A375968   n   a(n)  Digit average
%e A375968   --  ----  -------------
%e A375968    0     0              0
%e A375968    1     1              1
%e A375968    2     2              2
%e A375968    3     3              3
%e A375968    4     4              4
%e A375968    5     5              5
%e A375968    6     6              6
%e A375968    7     7              7
%e A375968    8     8              8
%e A375968    9     9              9
%e A375968   10    10            1/2
%e A375968   11     1              1
%e A375968   12    12            3/2
%e A375968   13     2              2
%e A375968   14    14            5/2
%e A375968   15     3              3
%t A375968 a[n_]:=Module[{k=0}, While[Mean[IntegerDigits[k]]!=Mean[IntegerDigits[n]], k++]; k]; Array[a,76,0] (* _Stefano Spezia_, Sep 07 2024 *)
%o A375968 (PARI) a(n, base = 10) = { my (d = digits(n, base), avg = vecsum(d) / max(1, #d)); if (avg==0, 0, my (t = vector(denominator(avg)), r = numerator(avg), x); t[1] = 1; r--; forstep (k = #t, 1, -1, t[k] += x = min(r, base-1); r -= x;); fromdigits(t, base);); }
%Y A375968 Cf. A007953, A055642, A342829, A375967, A375969.
%K A375968 nonn,base
%O A375968 0,3
%A A375968 _Rémy Sigrist_, Sep 04 2024