A316765 A self-"read and extend" sequence built following the three rules given in the Comments section.

1, 0, 2, 6, 18, 9, 27, 13, 39, 19, 9, 4, 2, 1, 0, 0, 0, 0, 0, 0, 3, 5, 7, 8, 10, 11, 5, 2, 1, 3, 1, 12, 6, 3, 1, 3, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 14, 15, 16, 17, 20, 21, 22, 23, 24, 12, 36, 18, 9, 4, 12, 6, 3, 9, 25, 75, 37, 111, 333, 999, 499, 1497, 4491, 2245, 6735, 3367, 10101, 5050, 15150, 7575

Offset: 1

Author

Eric Angelini and Jean-Marc Falcoz, Jul 12 2018

Keywords

• base
• nonn
• look

Comments

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

when the read digit is odd, we divide by 2 the last term of the sequence, then extend the sequence with the entire part of the result;

when the read digit is even (but not 0), we multiply by 3 the last term of the sequence, then extend the sequence with the result;

when the read digit is 0, we extend the sequence with the smallest integer not yet present in the sequence.

Examples

			The odd digit 1 divides 1 by two (which is 0,5), and |0,5| is 0;
the digit 0 extends the sequence with the smallest integer not present yet in the sequence, which is 2;
the digit 2 multiplies 2 by three, which is 6;
the digit 6 multiplies 6 by three, which is 18;
the odd digit 1 divides 18 by two, which is 9;
the digit 8 multiplies 9 by three, which is 27; etc.
		

Links

• Jean-Marc Falcoz, Table of n, a(n) for n = 1..10001

Crossrefs

Cf. (for more self-"read and extend" sequences) A316749, A316750, A316758, A316764.