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

1,1

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].

Links

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

Example

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.

Crossrefs

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

Sequence in context: A136853 A361911 A215287 * A331780 A360563 A290061

Adjacent sequences: A316761 A316762 A316763 * A316765 A316766 A316767

Keyword

base,nonn

Author

Eric Angelini and Jean-Marc Falcoz, Jul 12 2018

Status

approved