

A316764


A self"read and extend" sequence built following the rules visible in the Comments section (a kind of Collatzbydigits sequence).


3



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
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OFFSET

1,1


COMMENTS

Start with a(1) = 3 and read the sequence digitbydigit 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



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).


KEYWORD

base,nonn


AUTHOR



STATUS

approved



