A333398 -id:A333398 - cp's OEIS frontend

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

Alec Jones, Mar 18 2020

sign

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.

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

Cf. A333398, the partial sums of this sequence.

Cf. A328190 and A327460 for similar constructions.

A367264 a(n) = A367262(0) XOR ... XOR A367262(n) (where XOR denotes the bitwise XOR operator).

Original entry on oeis.org

0, 1, 3, 7, 4, 2, 5, 13, 8, 6, 15, 31, 21, 30, 18, 29, 16, 9, 24, 10, 25, 12, 26, 14, 22, 11, 28, 60, 38, 61, 33, 63, 32, 17, 48, 19, 49, 20, 50, 27, 51, 23, 59, 123, 92, 118, 93, 112, 94, 113, 65, 115, 64, 116, 66, 119, 79, 120, 67, 122, 70, 124, 62, 127, 58

Offset: 0

Rémy Sigrist, Nov 11 2023

All terms are distinct.

Will every nonnegative integer appear?

			a(2) = A367262(0) XOR A367262(1) XOR A367262(2) = 0 XOR 1 XOR 2 = 3.

Rémy Sigrist, Table of n, a(n) for n = 0..10000
Rémy Sigrist, C++ program

Cf. A333398, A367262.

cp's OEIS Frontend

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

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