A338478 Let b be an odd function such that b(0) = 0, b(1) = 1, and for any n > 1 such that 3^x < 2*n < 3^(x+1) for some x > 0, b(n) = b(3^x-n) - 3^x; a(n) = abs(b(n)) for any n >= 0.

0, 1, 2, 3, 4, 13, 12, 11, 8, 9, 10, 7, 6, 5, 32, 33, 34, 37, 36, 35, 38, 39, 40, 31, 30, 29, 26, 27, 28, 25, 24, 23, 14, 15, 16, 19, 18, 17, 20, 21, 22, 103, 102, 101, 98, 99, 100, 97, 96, 95, 104, 105, 106, 109, 108, 107, 110, 111, 112, 121, 120, 119, 116

Offset

0,3

Comments

This sequence is a self-inverse permutation of the nonnegative integers.

It is possible to build a continuous injective complex-valued function of a real-variable, say f, such that Im(f(r)) = 0 iff r is an integer and for any n in Z, f(n) = b(n) (see illustration in Links section).

Links

Rémy Sigrist, Table of n, a(n) for n = 0..6560

Rémy Sigrist, Representation in the complex plane of a function f as described in Comments section (the corresponding curve divides the complex plane into two simply connected regions rendered with different colors)

Index entries for sequences that are permutations of the natural numbers

Formula

a(n) = n iff abs(n - 3^x) <= 1 for some x >= 0.

Example

For n = 3:
- we have 3^1 < 2*3 < 3^(1+1),
- so b(3) = b(3 - 3) - 3 = 0 - 3 = -3,
- a(3) = abs(b(3)) = 3.

Prog

(PARI) b(n) = { if (n<0,  return (-b(-n)), n==0, return (0), n==1, return (1), for (x=1, oo, my (w=3^x, h=w\2); if (w<2*n && 2*n<3*w, return (b(w-n)-w)))) }
a(n) = abs(b(n))

Crossrefs

Cf. A000244, A003462, A024023, A034472, A105209.

Sequence in context: A328210 A303385 A325709 * A126129 A102947 A281512

Adjacent sequences: A338475 A338476 A338477 * A338479 A338480 A338481

Keyword

nonn

Author

Rémy Sigrist, Oct 29 2020

Status

approved