A375968 -id:A375968 - cp's OEIS frontend

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

11, 13, 15, 17, 19, 39, 59, 79, 99, 1001, 20, 21, 22, 23, 24, 25, 26, 27, 28, 102, 30, 31, 32, 33, 34, 35, 36, 37, 38, 1005, 40, 41, 42, 43, 44, 45, 46, 47, 48, 105, 50, 51, 52, 53, 54, 55, 56, 57, 58, 1009, 60, 61, 62, 63, 64, 65, 66, 67, 68, 108, 70, 71, 72

Offset: 1

Rémy Sigrist, Sep 04 2024

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

			The first terms, alongside the corresponding digit average, are:
  n   a(n)  Digit average
  --  ----  -------------
   1    11              1
   2    13              2
   3    15              3
   4    17              4
   5    19              5
   6    39              6
   7    59              7
   8    79              8
   9    99              9
  10  1001            1/2
  11    20              1
  12    21            3/2

Rémy Sigrist, Table of n, a(n) for n = 1..10000
Rémy Sigrist, PARI program

Cf. A007953, A055642, A228915, A375968.

a[n_]:=Module[{k=0}, While[k<=n || Mean[IntegerDigits[k]] != Mean[IntegerDigits[n]], k++]; k]; Array[a,63] (* Stefano Spezia, Sep 07 2024 *)

avg(n, base) = my (d = digits(n, base)); vecsum(d) / max(1, #d)
a(n, base = 10) = { my (v = avg(n, base)); for (m = n+1, oo, if (avg(m, base)==v, return (m););); }

PARI
```
\\ See Links section.
```

A375969 Lexicographically earliest sequence of nonnegative integers with distinct digit averages.

Original entry on oeis.org

0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 12, 14, 16, 18, 29, 49, 69, 89, 100, 101, 103, 104, 106, 107, 109, 119, 139, 149, 169, 179, 199, 299, 499, 599, 799, 899, 1000, 1002, 1004, 1006, 1008, 1019, 1039, 1059, 1079, 1099, 1299, 1499, 1699, 1899, 2999, 4999, 6999

Offset: 1

Rémy Sigrist, Sep 04 2024

Equivalently, fixed points of A375968.

The sequence {A007953(a(n)) / A055642(a(n)), n > 0} runs uniquely through every rational number between 0 and 9.

			The first terms, alongside the corresponding digit average, are:
  n   a(n)  Digit average
  --  ----  -------------
   1     0              0
   2     1              1
   3     2              2
   4     3              3
   5     4              4
   6     5              5
   7     6              6
   8     7              7
   9     8              8
  10     9              9
  11    10            1/2
  12    12            3/2
  13    14            5/2
  14    16            7/2
  15    18            9/2

Rémy Sigrist, Table of n, a(n) for n = 1..10459
Rémy Sigrist, PARI program

Cf. A007953, A051885, A055642, A375968.

kmax=7000; avg={}; list={}; For[k=0, k<=kmax, k++,mn=Mean[IntegerDigits[k]]; If[!MemberQ[avg,mn], AppendTo[avg, mn]; AppendTo[list, k]]]; list (* Stefano Spezia, Sep 07 2024 *)

avg(n, base = 10) = { my (d = digits(n, base)); vecsum(d) / max(1, #d) }
{ V = Map(); k = 0; for (n = 0, 6999, v = avg(n); if (!mapisdefined(V, v), mapput(V, v, n); print1 (n", "););); }

PARI
```
\\ See Links section.
```

from math import gcd
from itertools import count, islice
def agen():
    m = 0
    yield 0
    for w in count(1): # w = number of digits
        for s in range(1, 9*w+1): # s = sum of digits
            if gcd(s, w) == 1:
                d, r = [1] + [0 for _ in range(w-1)], s-1
                for k in range(w-1, -1, -1):
                    d[k], r = d[k] + min(r, 9), r - min(r, 9)
                yield int("".join(map(str, d)))
print(list(islice(agen(), 54)))
# Michael S. Branicky, Sep 08 2024 after Rémy Sigrist PARI in link

cp's OEIS Frontend

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

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A375969 Lexicographically earliest sequence of nonnegative integers with distinct digit averages.

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Programs

Mathematica

PARI

PARI

Python