A131881 Complement of A116700. Might be called "punctual birds".

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, 30, 33, 35, 36, 37, 38, 39, 40, 44, 46, 47, 48, 49, 50, 55, 57, 58, 59, 60, 66, 68, 69, 70, 77, 79, 80, 88, 90, 100, 102, 103, 104, 105, 106, 107, 108, 109, 113, 114

Offset

1,2

Comments

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

Every power of 10 is a member, which proves that the sequence is infinite. - N. J. A. Sloane, Jul 23 2007

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

Links

M. F. Hasler, Table of n, a(n) for n = 1..2428

Example

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

Prog

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

Crossrefs

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

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

Sequence in context: A318536 A048991 A321292 * A364728 A053460 A304678

Adjacent sequences: A131878 A131879 A131880 * A131882 A131883 A131884

Keyword

nonn,base,easy

Author

M. F. Hasler, Jul 23 2007

Status

approved