A338241 For any m >= 0, a(3*m) = 3*a(m), a(3*m+1) = 1-3*a(m), a(3*m+2) = 3*a(m)-1.

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

Offset: 0

Author

Rémy Sigrist, Oct 18 2020

Keywords

• sign

Comments

This sequence is a variant of A117966.

This sequence is a bijection from N = [0..+oo) to Z = (-oo..+oo).

Examples

			For n = 0:
- a(3*0) = 3*a(0),
- so a(0) = 0.
For n = 1:
- a(1) = 1 - 3*a(0) = 1.
For n = 2:
- a(2) = 3*a(0) - 1 = -1.
For n = 4:
- a(4) = 1 - 3*a(1) = -2.
		

Links

• Rémy Sigrist, Table of n, a(n) for n = 0..6560
• Rémy Sigrist, Scatterplot of the first 3^9 terms

Crossrefs

Cf. A005823, A117966, A338242-A338243 (bisections).

Programs

PARI

a(n) = { if (n==0, return (0), my (d=n%3, m=n\3); if (d==0, 3*a(m), d==1, 1-3*a(m), 3*a(m)-1)) }

Formula

Sum_{k = 0..n} a(k) >= 0 with equality iff n belongs to A005823.