Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).
%I #13 Jul 29 2013 08:19:59
%S 1,34,56,1222,1555,25554,29998,433330,7988888882,1101010101010,
%T 1222222222222,158585858585858,172727272727272,21515151515151514,
%U 23131313131313130,2797979797979797978,2979797979797979796,352525252525252525250,372727272727272727270
%N First occurrence of n consecutive n's in the decimal expansion of the Champernowne constant.
%C Earls sequence for the Champernowne constant.
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/ChampernowneConstantDigits.html">Champernowne Constant Digits</a>
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/EarlsSequence.html">Earls Sequence</a>
%e C = 0.12345678910111213141516171819202122232425262728293031323334..., so
%e a(1) = 1 (one 1 first appears at digit 1 after the decimal point),
%e a(2) = 34 (two 2s first occur starting at digit 34),
%e a(3) = 56 (three 3s first occur starting at digit 56).
%t 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 *)
%K nonn,base
%O 1,2
%A _Eric W. Weisstein_, Jul 24 2013
%E a(9) from _Eric W. Weisstein_, Jul 28 2013
%E a(10)-a(19) from _Giovanni Resta_, Jul 29 2013