A333400 Lexicographically earliest infinite sequence of distinct integers whose partial sums are all distinct integers.

0, -1, -2, 1, -3, -4, 2, 3, 5, 4, 6, -5, 7, -6, 8, -7, 9, -8, 10, -9, 11, 12, -10, -11, 13, 14, -12, -13, 15, 16, -14, -15, 18, -16, 17, 19, -17, 20, -19, -18, 21, 22, -20, -21, 24, -22, 23, 25, -23, 26, -24, -25, 27, 28, -26, -27, 30, -28, 29, 31, -29, 32

Offset: 1

Author

Alec Jones, Mar 18 2020

Keywords

• sign

Comments

This sequence is infinite. Consider first n partial sums; a distinct partial sum can always be formed by choosing a sufficiently large integer for a(n+1).

We organize lexicographically by magnitude, i.e., a precedes b if |a| < |b|; if |a| = |b|, then a precedes b if a < b.

Conjecture: This is a permutation of the integers.

Links

• Alec Jones, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A333398, the partial sums of this sequence.

Cf. A328190 and A327460 for similar constructions.