A355624 a(0) = 0, and for any n > 0, a(3*n) = 3*a(n), a(3*n+1) = 1-3*a(n), a(3*n+2) = 2-3*a(n).

0, 1, 2, 3, -2, -1, 6, -5, -4, 9, -8, -7, -6, 7, 8, -3, 4, 5, 18, -17, -16, -15, 16, 17, -12, 13, 14, 27, -26, -25, -24, 25, 26, -21, 22, 23, -18, 19, 20, 21, -20, -19, 24, -23, -22, -9, 10, 11, 12, -11, -10, 15, -14, -13, 54, -53, -52, -51, 52, 53, -48, 49

Offset

0,3

Comments

This sequence establishes a bijection from the nonnegative integers (N) to the integers (Z).

This sequence is to base 3 what A065620 is to base 2.

To compute a(n): write n as a sum of terms of A038754 with distinct 3-adic valuations and take the alternating sum.

Links

Rémy Sigrist, Table of n, a(n) for n = 0..6561

Formula

a(n) = n iff n = 0 or n belongs to A038754.

Example

For n = 107:
  107 = 3^4 + 2*3^2 + 2*3^1 + 2*3^0,
  so a(107) = -3^4 + 2*3^2 - 2*3^1 + 2*3^0 = -67.

Prog

(PARI) a(n, base=3) = { my (d=digits(n, base), s=1); forstep (k=#d, 1, -1, if (d[k], d[k]*=s; s=-s)); return (fromdigits(d, base)) }

Crossrefs

Cf. A038754, A065620, A355675.

Sequence in context: A370180 A286156 A113908 * A065369 A336404 A370182

Adjacent sequences: A355621 A355622 A355623 * A355625 A355626 A355627

Keyword

sign,base,easy

Author

Rémy Sigrist, Jul 14 2022

Status

approved