A368671 For any k >= 0, let P(k) = A368357(k) and P(-k) = A368358(k); for any n > 0, a(n) is the unique k such that P(k) = n.

0, 1, 2, -1, -3, -2, -4, 3, 7, 5, 9, 4, 8, 6, 10, -5, -13, -9, -17, -7, -15, -11, -19, -6, -14, -10, -18, -8, -16, -12, -20, 11, 27, 19, 35, 15, 31, 23, 39, 13, 29, 21, 37, 17, 33, 25, 41, 12, 28, 20, 36, 16, 32, 24, 40, 14, 30, 22, 38, 18, 34, 26, 42, -21

Offset: 1

Author

Rémy Sigrist, Jan 02 2024

Keywords

• sign
• look

Comments

This sequence is a bijection from the positive integers to the integers (Z).

Examples

			P(2) = A368357(2) = 3, so a(3) = 2.
P(-4) = A368358(4) = 7, so a(7) = -4.
		

Links

• Rémy Sigrist, Table of n, a(n) for n = 1..8191
• Rémy Sigrist, PARI program

Crossrefs

Cf. A368357, A368358.

Programs

PARI

\\ See Links section.

Formula

Conjecture: a(n) = (-1)^(L(n)+1)*(A001045(L(n)+2) - A036044(n)/2 - 1) for n > 0 where L(n) = A000523(n). - Mikhail Kurkov, Dec 13 2024