

A316749


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


6



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
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OFFSET

1,2


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.


LINKS



EXAMPLE

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.


CROSSREFS



KEYWORD



AUTHOR



STATUS

approved



