A224896 First occurrence of n consecutive n's in the decimal expansion of the Champernowne constant.

1, 34, 56, 1222, 1555, 25554, 29998, 433330, 7988888882, 1101010101010, 1222222222222, 158585858585858, 172727272727272, 21515151515151514, 23131313131313130, 2797979797979797978, 2979797979797979796, 352525252525252525250, 372727272727272727270

Offset

1,2

Comments

Earls sequence for the Champernowne constant.

Links

Table of n, a(n) for n=1..19.

Eric Weisstein's World of Mathematics, Champernowne Constant Digits

Eric Weisstein's World of Mathematics, Earls Sequence

Example

C = 0.12345678910111213141516171819202122232425262728293031323334..., so
a(1) = 1 (one 1 first appears at digit 1 after the decimal point),
a(2) = 34 (two 2s first occur starting at digit 34),
a(3) = 56 (three 3s first occur starting at digit 56).

Mathematica

r[d_, n_] := FromDigits@Flatten[IntegerDigits /@ Table[d, {n}]]; up[n_] := Block[{z = IntegerLength@n}, n*z + (10 - 10^z)/9]; Table[ If[n == 9, up[899999999] + 1, up[r[n, Floor[n/2] + 1]]], {n, 19}] (* Giovanni Resta, Jul 29 2013 *)

Crossrefs

Sequence in context: A055574 A294173 A176687 * A103558 A103686 A211715

Adjacent sequences: A224893 A224894 A224895 * A224897 A224898 A224899

Keyword

nonn,base

Author

Eric W. Weisstein, Jul 24 2013

Extensions

a(9) from Eric W. Weisstein, Jul 28 2013

a(10)-a(19) from Giovanni Resta, Jul 29 2013

Status

approved