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.

-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

Offset: 1

Author

Rémy Sigrist, Mar 05 2023

Keywords

• sign

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.

Examples

			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
		

Links

• Rémy Sigrist, PARI program

Crossrefs

Cf. A360305, A361144.

Programs

PARI

See Links section.