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A373096
a(n) = a([n/9]) + a([n/27]) + a([n/81]) + ..., where a(0) = 0, a(1) = 1, and [ ] = floor().
3
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
0,82
COMMENTS
Every term is a Fibonacci number, and every positive Fibonacci number occurs.
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.
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}]
PROG
(PARI) a(n) = if (n<=1, n, sum(k=2, n, a(n\3^k))); \\ Michel Marcus, Jun 01 2024
CROSSREFS
KEYWORD
nonn
AUTHOR
Clark Kimberling, May 31 2024
STATUS
approved