A132133 -id:A132133 - cp's OEIS frontend

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

M. F. Hasler, Jul 23 2007

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

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

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

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

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

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

A132131 "Punctual Bird" numbers n with the additional property that n-1 is not a Punctual Bird (cf. A131881).

Original entry on oeis.org

1, 13, 22, 24, 33, 35, 44, 46, 55, 57, 66, 68, 77, 79, 88, 90, 100, 102, 113, 124, 133, 143, 153, 163, 173, 183, 193, 203, 224, 235, 244, 254, 264, 274, 284, 294, 304, 335, 346, 355, 365, 375, 385, 395, 405, 446, 457, 466, 476, 486, 496, 506, 557, 568, 577, 587

Offset: 1

Graeme McRae, Aug 11 2007

Punctual Birds (A131881) are all numbers k with A132131(n) <= k < A132132(n) for some n Early Birds (A116700) are all numbers k with A132132(n) <= k < A132131(n+1) for some n

			a(1)=1 because 1 is the first Punctual Bird.
a(2)=13 because 1-11 are Punctual Birds and 12 is not a Punctual Bird.
a(3)=22 because 13-20 are Punctual Birds and 21 is not a Punctual Bird.

Graeme McRae, Table of n, a(n) for n = 1..27348

Cf. A033307, A117804, A116700, A131881, A132132, A132133.

A131981 Number of early bird numbers <= n.

Original entry on oeis.org

0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 3, 3, 3, 3, 3, 3, 3, 3, 4, 5, 5, 6, 6, 6, 6, 6, 6, 6, 7, 8, 9, 9, 10, 10, 10, 10, 10, 10, 11, 12, 13, 14, 14, 15, 15, 15, 15, 15, 16, 17, 18, 19, 20, 20, 21, 21, 21, 21, 22, 23, 24, 25, 26, 27, 27, 28, 28, 28, 29, 30, 31, 32

Offset: 1

Klaus Brockhaus, Aug 15 2007

a(n) = number of k such that A116700(k) <= n; a(n) = n - number of k such that A131881(k) <= n.

A131982 gives numbers n such that a(n) = n/2, or numbers n such that (number of k such that A116700(k) <= n) = (number of k such that A131881(k) <= n).

			There are two early bird numbers <= 21, viz. 12 and 21, hence a(21) = 2.

Klaus Brockhaus, Table of n, a(n) for n = 1..6000
Klaus Brockhaus, Plots of A131981(n)/n at various scales

Cf. A116700 (early bird numbers), A131881 (complement of A116700), A132133 (number of n-digit terms of 131881), A105390 (number of Rollman numbers <= n), A131982 (numbers n such that A131981(n) = n/2).

s$ = "" : d = 0
FOR n = 1 TO 84
sn$ = str$(n)
IF instr(s$, sn$) > 0 THEN d = d+1
s$ = s$ + sn$ : print d ; ",";
NEXT

A132132 "Early Bird" numbers n such that n-1 is not an Early Bird (cf. A116700).

Original entry on oeis.org

12, 21, 23, 31, 34, 41, 45, 51, 56, 61, 67, 71, 78, 81, 89, 91, 101, 110, 121, 131, 141, 151, 161, 171, 181, 191, 201, 210, 231, 241, 251, 261, 271, 281, 291, 301, 310, 341, 351, 361, 371, 381, 391, 401, 410, 451, 461, 471, 481, 491, 501, 510, 561, 571, 581

Offset: 1

Graeme McRae, Aug 11 2007

Punctual Birds (A131881) are all numbers k with A132131(n) <= k < A132132(n) for some n Early Birds (A116700) are all numbers k with A132132(n) <= k < A132131(n+1) for some n

			a(1)=12 because 12 is the first Early Bird.
a(2)=21 because 21 is the second Early Bird.
a(3)=23 because 23 is the third Early Bird.
a(4)=31 because 31 is the fourth Early Bird.
a(5)=34 because 31-32 are Early Birds and 33 is not an Early Bird.

Graeme McRae, Table of n, a(n) for n = 1..27348

Cf. A033307, A117804, A116700, A131881, A132131, A132133.

A132134 Base 3 "Punctual Bird" numbers: write the natural numbers, base 3, in a string 12101112202122100101102... Sequence gives numbers which do not occur in the string ahead of their natural place.

Original entry on oeis.org

1, 2, 3, 4, 6, 9, 11, 15, 18, 27, 29, 30, 32, 33, 35, 42, 45, 54, 60, 81, 83, 86, 87, 89, 92, 95, 96, 98, 99, 101, 104, 105, 107, 123, 126, 135, 141, 153, 162, 243, 245, 248, 249, 251, 252, 254, 257, 258, 260, 261, 263, 266, 267, 269, 275, 276, 278, 285, 287, 288

Offset: 1

Graeme McRae, Aug 11 2007

			a(5)=6 because 6 (20, base 3) is the fifth number that appears first in its "natural" place in the string of concatenated base-3 numbers.

Cf. A033307, A117804, A116700, A131881, A132131, A132132, A132133, A132135.

cp's OEIS Frontend

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

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A132131 "Punctual Bird" numbers n with the additional property that n-1 is not a Punctual Bird (cf. A131881).

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A131981 Number of early bird numbers <= n.

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A132132 "Early Bird" numbers n such that n-1 is not an Early Bird (cf. A116700).

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A132134 Base 3 "Punctual Bird" numbers: write the natural numbers, base 3, in a string 12101112202122100101102... Sequence gives numbers which do not occur in the string ahead of their natural place.

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