A131881 - OEIS

%I #12 Oct 25 2019 12:39:18

%S 1,2,3,4,5,6,7,8,9,10,11,13,14,15,16,17,18,19,20,22,24,25,26,27,28,29,

%T 30,33,35,36,37,38,39,40,44,46,47,48,49,50,55,57,58,59,60,66,68,69,70,

%U 77,79,80,88,90,100,102,103,104,105,106,107,108,109,113,114

%N Complement of A116700. Might be called "punctual birds".

%C Numbers n that do not occur in the concatenation of 1,2,3...,n-1.

%C Every power of 10 is a member, which proves that the sequence is infinite. - _N. J. A. Sloane_, Jul 23 2007

%C The asymptotic density of the sequence is zero. The number of k-digit terms is A132133 = (9, 45, 270, 2104, ...), k = 1, 2, .... These are the first difference of the indices of powers of 10, T = (1, 10, 55, 325, 2429, ...), which we get as partial sums if we prefix A132133(0) = 1 corresponding to the number 0. - _M. F. Hasler_, Oct 24 2019

%H M. F. Hasler, <a href="/A131881/b131881.txt">Table of n, a(n) for n = 1..2428</a>

%e The first number not in this sequence is the early bird "12" which occurs as concatenation of 1 and 2.

%o (PHP) $s="0"; for(; ++$i < 2000; $s .= $i) if( !strpos($s,"$i")) echo $i,", ";

%Y Cf. A116700 (early birds), A132133 (number of n-digit terms).

%Y Cf. A007376 (Barbier word ...,8,9,1,0,1,1,...), A033307 (Champernowne constant).

%K nonn,base,easy

%O 1,2

%A _M. F. Hasler_, Jul 23 2007