A316764 A self-"read and extend" sequence built following the rules visible in the Comments section (a kind of Collatz-by-digits sequence).

3, 10, 31, 15, 46, 139, 418, 1255, 627, 313, 940, 2821, 8464, 4232, 12697, 6348, 19045, 9522, 28567, 85702, 42851, 21425, 64276, 192829, 578488, 1735465, 5206396, 2603198, 1301599, 650799, 325399, 162699, 488098, 244049, 122024, 61012, 30506, 15253, 7626, 22879, 11439, 34318, 17159

Offset: 1

Author

Eric Angelini and Jean-Marc Falcoz, Jul 12 2018

Keywords

• base
• nonn

Comments

Start with a(1) = 3 and read the sequence digit-by-digit starting from the left:

when the read digit is odd, we triple the last term of the sequence and add 1, then extend the sequence with the result;

when the read digit is even, we divide by 2 the last term of the sequence, then extend the sequence with the entire part of the result. Starting the sequence with a(1) = 1 or a(1) = 2 would generate the infinite (and rather uninteresting) sequence 1,4,2,1,4,2,1,4,2,1,4,2,1,...

It is not known by the authors if the sequence starting with a(1) = 3 comes back to 1, enters in another loop than [1,4,2,1] or extends itself forever [note that a(3000) has more than 300 digits].

Examples

			The odd digit 3 multiplies 3 by three (which is 9), and 9 plus 1 is 10;
the odd digit 1 multiplies 10 by three (which is 30), and 30 plus 1 is 31;
the even digit 0 divides 31 by two (which is 15,5), and |15,5| is 15;
the odd digit 3 multiplies 15 by three (which is 45), and 45plus 1 is 46;
the odd digit 1 multiplies 46 by three (which is 138), and 138 plus 1 is 139; etc.
		

Links

• Jean-Marc Falcoz, Table of n, a(n) for n = 1..3001

Crossrefs

Cf. A006370 (The Collatz or 3x+1 map: a(n) = n/2 if n is even, 3n + 1 if n is odd).