A334889 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, 0, 0, 1, 2, 2, 2, 1 for k = 0..7, respectively.

0, 0, 0, 1, 2, 2, 2, 1, 0, 0, 0, 1, 2, 2, 2, 1, 0, 0, 0, 1, 2, 2, 2, 1, 3, 3, 3, 4, 5, 5, 5, 4, 6, 6, 6, 7, 8, 8, 8, 7, 6, 6, 6, 7, 8, 8, 8, 7, 6, 6, 6, 7, 8, 8, 8, 7, 3, 3, 3, 4, 5, 5, 5, 4, 0, 0, 0, 1, 2, 2, 2, 1, 0, 0, 0, 1, 2, 2, 2, 1, 0, 0, 0, 1, 2, 2, 2

Offset

0,5

Comments

The lattice points with coordinates (A334888(n), a(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)

Wikipedia, Sierpinski carpet

Formula

A153490(1 + A334888(n), 1 + a(n)) = 1.

Example

For n = 42:
- 42 = 5*8^1 + 2*8^0,
- so a(42) = f(5)*3^1 + f(2)*3^0 = 2*3^1 + 0*3^0 = 6.

Prog

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

Crossrefs

Cf. A153490, A334888.

Sequence in context: A262372 A292520 A131079 * A078336 A076441 A319289

Adjacent sequences: A334886 A334887 A334888 * A334890 A334891 A334892

Keyword

nonn,base

Author

Rémy Sigrist, May 14 2020

Status

approved