A316909 A self-"read and extend" sequence built following the three rules visible in the Comments section (a variation of A316765).

1, 0, 2, 14, 4, 28, 196, 1372, 9604, 3201, 1067, 7469, 2489, 829, 276, 1932, 644, 4508, 3, 21, 7, 49, 5, 1, 0, 6, 42, 14, 4, 28, 196, 65, 455, 3185, 22295, 7431, 52017, 364119, 121373, 849611, 283203, 1982421, 660807, 220269, 73423, 513961, 3597727, 25184089, 176288623, 1234020361, 411340120, 8, 56

Offset: 1

Author

Eric Angelini and Jean-Marc Falcoz, Jul 16 2018

Keywords

• base
• nonn

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 3 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 7 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.

This is a possible variation among many others of the first 2 rules illustrated by A316765 (where an odd digit divides by 3 and an even digit -except 0— multiplies by 2) that shows the flexibility of the "read-and-extend" idea.

Examples

			Reading the sequence one digit after the other, starting from the left:
the odd digit 1 divides 1 by three (which is 0,333...), and |0,333...| 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 seven, which is 14;
the odd digit 1 divides 14 by three, (which is 4,666...) and |4,666...| is 4;
the digit 4 multiplies 4 by seven, which is 28;
the digit 4 multiplies 28 by seven, which is 196;
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 and A316765.