|
%I #12 Nov 13 2018 00:28:11
%S 3,10,31,15,46,139,418,1255,627,313,940,2821,8464,4232,12697,6348,
%T 19045,9522,28567,85702,42851,21425,64276,192829,578488,1735465,
%U 5206396,2603198,1301599,650799,325399,162699,488098,244049,122024,61012,30506,15253,7626,22879,11439,34318,17159
%N A self-"read and extend" sequence built following the rules visible in the Comments section (a kind of Collatz-by-digits sequence).
%C Start with a(1) = 3 and read the sequence digit-by-digit starting from the left:
%C when the read digit is odd, we triple the last term of the sequence and add 1, then extend the sequence with the result;
%C 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,...
%C 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].
%H Jean-Marc Falcoz, <a href="/A316764/b316764.txt">Table of n, a(n) for n = 1..3001</a>
%e The odd digit 3 multiplies 3 by three (which is 9), and 9 plus 1 is 10;
%e the odd digit 1 multiplies 10 by three (which is 30), and 30 plus 1 is 31;
%e the even digit 0 divides 31 by two (which is 15,5), and |15,5| is 15;
%e the odd digit 3 multiplies 15 by three (which is 45), and 45plus 1 is 46;
%e the odd digit 1 multiplies 46 by three (which is 138), and 138 plus 1 is 139; etc.
%Y Cf. A006370 (The Collatz or 3x+1 map: a(n) = n/2 if n is even, 3n + 1 if n is odd).
%K base,nonn
%O 1,1
%A _Eric Angelini_ and _Jean-Marc Falcoz_, Jul 12 2018
|
