|
%I #9 Jun 07 2024 06:42:29
%S 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,
%T 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,
%U 0,0,0,0,0,0,0,0,0,0,0,0,0,2,2,2,2,2
%N a(n) = a([n/9]) + a([n/27]) + a([n/81]) + ..., where a(0) = 0, a(1) = 1, and [ ] = floor().
%C Every term is a Fibonacci number, and every positive Fibonacci number occurs.
%F 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.
%p A373096 := proc(n)
%p option remember;
%p if n <=1 then
%p n;
%p else
%p add( procname(floor(n/3^k)),k=2..n) ;
%p end if;
%p end proc:
%p seq(A373096(n),n=0..100) ; # _R. J. Mathar_, Jun 07 2024
%t a[0] = 0; a[1] = 1;
%t a[n_] := a[n] = Sum[a[Floor[n/3^k]], {k, 2, n}]
%t Table[a[n], {n, 0, 570}]
%o (PARI) a(n) = if (n<=1, n, sum(k=2, n, a(n\3^k))); \\ _Michel Marcus_, Jun 01 2024
%Y Cf. A000045, A000244, A373095, A373097.
%K nonn
%O 0,82
%A _Clark Kimberling_, May 31 2024
|
