A346544 Indices of repeated digits of Champernowne's constant.

13, 14, 35, 36, 57, 58, 79, 80, 101, 102, 123, 124, 145, 146, 167, 168, 170, 189, 192, 196, 221, 224, 225, 226, 227, 230, 233, 236, 239, 242, 245, 248, 256, 258, 286, 291, 316, 324, 346, 357, 376, 390, 406, 423, 436, 456, 466, 489, 492, 499, 525, 529, 551, 554

Offset

1,1

Comments

In simpler terms, the sequence indexes where digits repeat when the natural numbers are written out in base 10.

Links

Harvey P. Dale, Table of n, a(n) for n = 1..1000

Example

   N  | N-th digit | Is digit     ||  N  | N-th digit | Is digit     ||
      | of A033307 | the same     ||     | of A033307 | the same     ||
      |            | as previous? ||     |            | as previous? ||
-------------------------------------------------------------------------
      |            |              ||     |            |              ||
    1 |     1      |    No        ||  21 |     5      |    No        ||
    2 |     2      |    No        ||  22 |     1      |    No        ||
    3 |     3      |    No        ||  23 |     6      |    No        ||
    4 |     4      |    No        ||  24 |     1      |    No        ||
    5 |     5      |    No        ||  25 |     7      |    No        ||
    6 |     6      |    No        ||  26 |     1      |    No        ||
    7 |     7      |    No        ||  27 |     8      |    No        ||
    8 |     8      |    No        ||  28 |     1      |    No        ||
    9 |     9      |    No        ||  29 |     9      |    No        ||
   10 |     1      |    No        ||  30 |     2      |    No        ||
   11 |     0      |    No        ||  31 |     0      |    No        ||
   12 |     1      |    No        ||  32 |     2      |    No        ||
   13 |     1      |    Yes       ||  33 |     1      |    No        ||
   14 |     1      |    Yes       ||  34 |     2      |    No        ||
   15 |     2      |    No        ||  35 |     2      |    Yes       ||
   16 |     1      |    No        ||  36 |     2      |    Yes       ||
   17 |     3      |    No        ||  37 |     3      |    No        ||
   18 |     1      |    No        ||  38 |     2      |    No        ||
   19 |     4      |    No        ||  39 |     4      |    No        ||
   20 |     1      |    No        ||  40 |     2      |    No        ||

Mathematica

f[n_]:=Last@First@RealDigits[ChampernowneNumber[], 10, n];
Select[Range@554, f[#]==f[#+1]&]+1 (* Giorgos Kalogeropoulos, Sep 17 2021 *)
SequencePosition[RealDigits[ChampernowneNumber[], 10, 600][[1]], {x_, x_}][[;; , 1]]+1 (* Harvey P. Dale, May 25 2026 *)

Prog

(Python)
x = ''
x = ''.join([x+str(k) for k in range(0, 100)])
print(', '.join([str(i) for i in [k for k in range(1, len(x)) if x[k] == x[k-1]]]))

Crossrefs

Cf. A033307.

Sequence in context: A308122 A292116 A071870 * A041350 A041348 A041346

Adjacent sequences: A346541 A346542 A346543 * A346545 A346546 A346547

Keyword

nonn,base,easy

Author

Alfred Holton-Stoppani, Sep 16 2021

Status

approved