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%I #24 Nov 01 2021 01:19:14
%S 13,14,35,36,57,58,79,80,101,102,123,124,145,146,167,168,170,189,192,
%T 196,221,224,225,226,227,230,233,236,239,242,245,248,256,258,286,291,
%U 316,324,346,357,376,390,406,423,436,456,466,489,492,499,525,529,551,554
%N Indices of repeated digits of Champernowne's constant.
%C In simpler terms, the sequence indexes where digits repeat when the natural numbers are written out in base 10.
%e N | N-th digit | Is digit || N | N-th digit | Is digit ||
%e | of A033307 | the same || | of A033307 | the same ||
%e | | as previous? || | | as previous? ||
%e -------------------------------------------------------------------------
%e | | || | | ||
%e 1 | 1 | No || 21 | 5 | No ||
%e 2 | 2 | No || 22 | 1 | No ||
%e 3 | 3 | No || 23 | 6 | No ||
%e 4 | 4 | No || 24 | 1 | No ||
%e 5 | 5 | No || 25 | 7 | No ||
%e 6 | 6 | No || 26 | 1 | No ||
%e 7 | 7 | No || 27 | 8 | No ||
%e 8 | 8 | No || 28 | 1 | No ||
%e 9 | 9 | No || 29 | 9 | No ||
%e 10 | 1 | No || 30 | 2 | No ||
%e 11 | 0 | No || 31 | 0 | No ||
%e 12 | 1 | No || 32 | 2 | No ||
%e 13 | 1 | Yes || 33 | 1 | No ||
%e 14 | 1 | Yes || 34 | 2 | No ||
%e 15 | 2 | No || 35 | 2 | Yes ||
%e 16 | 1 | No || 36 | 2 | Yes ||
%e 17 | 3 | No || 37 | 3 | No ||
%e 18 | 1 | No || 38 | 2 | No ||
%e 19 | 4 | No || 39 | 4 | No ||
%e 20 | 1 | No || 40 | 2 | No ||
%t f[n_]:=Last@First@RealDigits[ChampernowneNumber[],10,n];
%t Select[Range@554,f[#]==f[#+1]&]+1 (* _Giorgos Kalogeropoulos_, Sep 17 2021 *)
%o (Python)
%o x = ''
%o x = ''.join([x+str(k) for k in range(0,100)])
%o print(','.join([str(i) for i in [k for k in range(1,len(x)) if x[k] == x[k-1]]]))
%Y Cf. A033307.
%K nonn,base,easy
%O 1,1
%A _Alfred Holton-Stoppani_, Sep 16 2021