A316749 A self-"read and extend" sequence built following the rules given in the Comments section.

1, 2, 4, 8, 16, 15, 30, 29, 58, 57, 56, 112, 224, 223, 446, 445, 890, 889, 1778, 1777, 3, 6, 5, 7, 14, 13, 9, 18, 36, 10, 20, 19, 11, 22, 44, 88, 87, 174, 12, 24, 23, 46, 17, 34, 33, 66, 21, 25, 24, 48, 47, 94, 93, 186, 185, 370, 740, 739, 1478, 1477, 2954, 2953, 2952, 5904, 5903, 11806, 23612, 23611, 26, 52

Offset: 1

Author

Eric Angelini and Jean-Marc Falcoz, Jul 12 2018

Keywords

• base
• nonn
• look

Comments

Start with a(1) = 1 and a(2) = 2; read the sequence digit by digit starting from the left:

when the read digit is smaller than the next one, multiply by 2 the last integer of the sequence and extend it with the result;

when the read digit is bigger than the next one, subtract 1 from the last integer of the sequence and extend it with the result;

when both digits are equal, extend the sequence with the smallest integer not present so far.

Examples

			As the only digit of a(1) = 1 is smaller than 2 (the next digit), we extend the sequence with 4 (that is, 2 times 2);
as the only digit of a(2) = 2 is smaller than 4 (the next digit), we extend the sequence with 8 (that is, 2 times 4);
as the only digit of a(3) = 4 is smaller than 8 (the next digit), we extend the sequence with 16 (that is, 2 times 8);
as the only digit of a(4) = 8 is bigger than 1 (the next digit), we extend the sequence with 15 (that is, 16 minus 1);
as the first digit of a(5) = 1 is smaller than 6 (the next digit), we extend the sequence with 30 (that is, 2 times 15);
as the last digit of a(5) = 6 is bigger than 1 (the next digit), we extend the sequence with 29 (that is, 30 minus 1);
...
as the first digit of a(12) = 1 is equal to 1 (the next digit), we extend the sequence with 3 (this is the smallest integer not yet present in the sequence and is written after a(23) = 1777);
etc.
		

Links

• Jean-Marc Falcoz, Table of n, a(n) for n = 1..10002