A361189 Infinite sequence of nonzero integers build the greedy way such that the sums Sum_{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, -1, -4, -3, -6, 4, -11, 5, 6, 7, 8, -8, -12, 9, 21, -10, -13, 12, 25, 13, 16, -14, 31, -15, -17, 19, 33, -19, -21, 22, 41, -22, -24, 24, 49, -25, -26, -27, -28, 28, 34, -29, 61, -30, -31, -33, -34, 35, 39, -35, 75, -36, -37, 38, 77, -38, -39, -41, -42

Offset: 1

Author

Rémy Sigrist, Mar 03 2023

Keywords

• sign

Comments

This sequence is a variant of A361144 where we allows negative values.

In order for the sequence to be infinite, zero sums are forbidden.

We can arrange the terms of the sequence as the leaves of a perfect infinite binary tree, the sums with e > 0 corresponding to parent nodes; each node will contain a different value and all nonzero values will appear in the tree.

Examples

			The first terms (at the bottom of the tree) alongside the corresponding sums are:
                                18
                 ---------------------------------
                -18                             36
         -----------------               -----------------
        -2              -16             26              10
     ---------       ---------       ---------       ---------
     3      -5      -9      -7      11      15      -20     30
   -----   -----   -----   -----   -----   -----   -----   -----
   1   2  -1  -4  -3  -6   4 -11   5   6   7   8  -8 -12   9  21
		

Links

• Rémy Sigrist, Table of n, a(n) for n = 1..10000
• Rémy Sigrist, C++ program

Crossrefs

Cf. A361144.