A334888 a(n) = Sum_{k >= 0} f(d_k) * 3^k where Sum_{k >= 0} d_k * 8^k is the base 8 representation of n and f(k) = 0, 1, 2, 2, 2, 1, 0, 0 for k = 0..7, respectively.

0, 1, 2, 2, 2, 1, 0, 0, 3, 4, 5, 5, 5, 4, 3, 3, 6, 7, 8, 8, 8, 7, 6, 6, 6, 7, 8, 8, 8, 7, 6, 6, 6, 7, 8, 8, 8, 7, 6, 6, 3, 4, 5, 5, 5, 4, 3, 3, 0, 1, 2, 2, 2, 1, 0, 0, 0, 1, 2, 2, 2, 1, 0, 0, 9, 10, 11, 11, 11, 10, 9, 9, 12, 13, 14, 14, 14, 13, 12, 12, 15, 16

Offset

0,3

Comments

The lattice points with coordinates (a(n), A334889(n)) for n >= 0 form a Sierpinski carpet.

Links

Rémy Sigrist, Table of n, a(n) for n = 0..4095 (n = 0..8^4-1)

Rémy Sigrist, Colored scatterplot of (a(n), A334889(n)) for n = 0..8^6-1 (where the hue is function of n)

Wikipedia, Sierpinski carpet

Formula

A153490(1 + a(n), 1 + A334889(n)) = 1.

Example

For n = 42:
- 42 = 5*8^1 + 2*8^0,
- so a(42) = f(5)*3^1 + f(2)*3^0 = 1*3^1 + 2*3^0 = 5.

Prog

(PARI) a(n) = { my (f=[0, 1, 2, 2, 2, 1, 0, 0], d=Vecrev(digits(n, #f))); sum(k=0, #d-1, f[1+d[1+k]] * 3^k) }

Crossrefs

Cf. A153490, A334889.

Sequence in context: A076441 A319289 A124747 * A039981 A006140 A072931

Adjacent sequences: A334885 A334886 A334887 * A334889 A334890 A334891

Keyword

nonn,base

Author

Rémy Sigrist, May 14 2020

Status

approved