A277861 A self-describing sequence: the zeros and ones in the decimal representation of the sequence correspond to the binary representation of the sequence.

1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 20, 22, 23, 24, 25, 26, 27, 28, 29, 30, 13, 32, 33, 34, 35, 36, 37, 38, 39, 40, 14, 15, 16, 42, 43, 44, 45, 46, 47, 48, 49, 50, 17, 18, 19, 21, 52, 53, 54, 55, 56, 57, 58, 59, 60, 62, 63, 64, 65, 66, 67, 68, 69, 70, 72

Offset

1,2

Comments

The sequence is always extended with the smallest integer not yet present and not leading to a contradiction.

Numbers with neither 0 nor 1 in their decimal representation appear in increasing order.

Comments from N. J. A. Sloane, Nov 10 2016: (Start)

Here is another way to state the condition that the sequence must satisfy.

For each n, let D denote the concatenation of the first n terms in base 10, and let B denote the concatenation of the first n terms in base 2. Let D' be obtained from D by deleting all digits except 0 and 1.

Then D' must be a prefix of B.

In the examples below, D' appears in parentheses.

A278030 shows indices where the sequence changes from on or below the diagonal (a(n)<=n) to above the diagonal (a(n)>n), or vice versa. (End)

Links

Rémy Sigrist, Table of n, a(n) for n = 1..10000

Rémy Sigrist, PERL program for A277861

Example

When computing the sequence, we must check that for any n > 0, the zeros and ones among the decimal representation of the first n terms match the beginning of the binary representation of these terms.
The following table depicts the first terms, alongside their binary representation, and the matching zeros and ones among their decimal representation (in parentheses):
n   a(n)  a(n) in binary  First n terms in binary
--  ----  --------------  -----------------------
1   1     1               (1)
2   2     10              (1)10
3   3     11              (1)1011
4   4     100             (1)1011100
5   5     101             (1)1011100101
6   6     110             (1)1011100101110
7   7     111             (1)1011100101110111
8   8     1000            (1)10111001011101111000
9   9     1001            (1)101110010111011110001001
10  10    1010            (110)11100101110111100010011010
11  11    1011            (11011)1001011101111000100110101011
12  12    1100            (110111)0010111011110001001101010111100
13  20    10100           (1101110)01011101111000100110101011110010100

Crossrefs

Cf. A007088, A278030.

Sequence in context: A227508 A246200 A262356 * A173902 A261370 A257737

Adjacent sequences: A277858 A277859 A277860 * A277862 A277863 A277864

Keyword

nonn,base

Author

Rémy Sigrist, Nov 02 2016

Status

approved