|
%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
| 