A373096 a(n) = a([n/9]) + a([n/27]) + a([n/81]) + ..., where a(0) = 0, a(1) = 1, and [ ] = floor().

0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, 2

Offset: 0

Author

Clark Kimberling, May 31 2024

Keywords

• nonn

Comments

Every term is a Fibonacci number, and every positive Fibonacci number occurs.

Crossrefs

Cf. A000045, A000244, A373095, A373097.

Programs

Maple

A373096 := proc(n)
    option remember;
    if n <=1 then
        n;
    else
        add( procname(floor(n/3^k)),k=2..n) ;
    end if;
end proc:
seq(A373096(n),n=0..100) ; # R. J. Mathar, Jun 07 2024

Mathematica

a[0] = 0; a[1] = 1;
a[n_] := a[n] = Sum[a[Floor[n/3^k]], {k, 2, n}]
Table[a[n], {n, 0, 570}]

PARI

a(n) = if (n<=1, n, sum(k=2, n, a(n\3^k))); \\ Michel Marcus, Jun 01 2024

Formula

Following the first 3^2 terms (all zeros and ones): 3^2 ones, 3^2 zeros, 3^3 ones, 3^3 zeros, 3^4 twos, 3^4 zeros, 3^5 threes, 3^5 zeros, 3^6 fives, 3^6 zeros, etc.