|
|
A361234
|
|
Infinite sequence of nonzero integers build the greedy way such that the products Product_{i = k*2^e..(k+1)*2^e} a(i) with k, e >= 0 are all distinct; each term is minimal in absolute value and in case of a tie, preference is given to the positive value.
|
|
3
|
|
|
-1, 2, 3, -3, 4, -4, 5, -5, 6, -6, 7, -7, 8, -8, 9, 10, -10, 11, -11, 12, -12, 13, -13, 14, -14, 15, -15, 16, 17, -17, -18, 19, -19, 20, -20, 21, -21, 22, -22, 23, -23, 24, -24, 25, 26, -26, 27, -27, 28, -28, 29, -29, 30, -30, 31, -31, 32, -32, 33, -33, 34
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
1,2
|
|
COMMENTS
|
This sequence is a variant of A360305 where we allow negative values.
In order for the sequence to be infinite, the value 1 is forbidden.
We can arrange the terms of the sequence as the leaves of a perfect infinite binary tree, the products with e > 0 corresponding to parent nodes; each node will contain a different value and all values except 0 and 1 will appear in the tree.
|
|
LINKS
|
|
|
EXAMPLE
|
The first terms (at the bottom of the tree) alongside the corresponding products are:
-73156608000
---------------------------------
7200 -10160640
----------------- -----------------
18 400 1764 -5760
--------- --------- --------- ---------
-2 -9 -16 -25 -36 -49 -64 90
----- ----- ----- ----- ----- ----- ----- -----
-1 2 3 -3 4 -4 5 -5 6 -6 7 -7 8 -8 9 10
|
|
PROG
|
(PARI) See Links section.
|
|
CROSSREFS
|
|
|
KEYWORD
|
sign
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|