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A131881
Complement of A116700. Might be called "punctual birds".
12
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
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
KEYWORD
nonn,base,easy
AUTHOR
M. F. Hasler, Jul 23 2007
STATUS
approved