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

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, 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, 29, 6, 49, 7, 3, 16, 4, 18, 5, 29, 6, 49, 7, 69, 16, 4, 18, 5, 29, 6

Offset: 0

Author

Rémy Sigrist, Sep 04 2024

Keywords

• nonn
• base

Comments

The digit average of a number n is its sum of digits divided by its number of digits: A007953(n) / A055642(n).

Examples

			The first terms, alongside the corresponding digit average, are:
  n   a(n)  Digit average
  --  ----  -------------
   0     0              0
   1     1              1
   2     2              2
   3     3              3
   4     4              4
   5     5              5
   6     6              6
   7     7              7
   8     8              8
   9     9              9
  10    10            1/2
  11     1              1
  12    12            3/2
  13     2              2
  14    14            5/2
  15     3              3
		

Links

• Rémy Sigrist, Table of n, a(n) for n = 0..10000

Crossrefs

Cf. A007953, A055642, A342829, A375967, A375969.

Programs

Mathematica

a[n_]:=Module[{k=0}, While[Mean[IntegerDigits[k]]!=Mean[IntegerDigits[n]], k++]; k]; Array[a,76,0] (* Stefano Spezia, Sep 07 2024 *)

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);); }