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A375967 a(n) is the least number > n with the same digit average as n.

%I A375967 #11 Sep 08 2024 07:54:20
%S A375967 11,13,15,17,19,39,59,79,99,1001,20,21,22,23,24,25,26,27,28,102,30,31,
%T A375967 32,33,34,35,36,37,38,1005,40,41,42,43,44,45,46,47,48,105,50,51,52,53,
%U A375967 54,55,56,57,58,1009,60,61,62,63,64,65,66,67,68,108,70,71,72
%N A375967 a(n) is the least number > n with the same digit average as n.
%C A375967 The digit average of a number n is its sum of digits divided by its number of digits: A007953(n) / A055642(n).
%H A375967 Rémy Sigrist, <a href="/A375967/b375967.txt">Table of n, a(n) for n = 1..10000</a>
%H A375967 Rémy Sigrist, <a href="/A375967/a375967.gp.txt">PARI program</a>
%e A375967 The first terms, alongside the corresponding digit average, are:
%e A375967   n   a(n)  Digit average
%e A375967   --  ----  -------------
%e A375967    1    11              1
%e A375967    2    13              2
%e A375967    3    15              3
%e A375967    4    17              4
%e A375967    5    19              5
%e A375967    6    39              6
%e A375967    7    59              7
%e A375967    8    79              8
%e A375967    9    99              9
%e A375967   10  1001            1/2
%e A375967   11    20              1
%e A375967   12    21            3/2
%t A375967 a[n_]:=Module[{k=0}, While[k<=n || Mean[IntegerDigits[k]] != Mean[IntegerDigits[n]], k++]; k]; Array[a,63] (* _Stefano Spezia_, Sep 07 2024 *)
%o A375967 (PARI) avg(n, base) = my (d = digits(n, base)); vecsum(d) / max(1, #d)
%o A375967 a(n, base = 10) = { my (v = avg(n, base)); for (m = n+1, oo, if (avg(m, base)==v, return (m););); }
%o A375967 (PARI) \\ See Links section.
%Y A375967 Cf. A007953, A055642, A228915, A375968.
%K A375967 nonn,base,easy
%O A375967 1,1
%A A375967 _Rémy Sigrist_, Sep 04 2024