A305876 - OEIS

%I #21 Jun 14 2018 15:29:19

%S 1,2,5,16,36,84,273,648,2114,4757,16516,37161,87045,282896,673924,

%T 2184233,5263877,17107472,38830244,134554132,303080705,707272770,

%U 2300725397,5457925252,17805431433,42970665029,139654661284,314223120404,1099646108737,2474203744786

%N a(n) = Fibbinary(2^n).

%H Alois P. Heinz, <a href="/A305876/b305876.txt">Table of n, a(n) for n = 0..2306</a>

%F a(n) = A003714(2^n).

%F A014417(2^n) = A007088(a(n)).

%e a(6) = A003714(2^6) = A003714(64) = 273 = 100010001_2 because F(0+2) + F(4+2) + F(8+2) = 1 + 8 + 55 = 64, where 0, 4, 8 are the indices of 1 bits in 100010001_2.  A014417(64) = 100010001 = A007088(273).

%p F:= proc(n) F(n):= `if`(n<2, n, F(n-1)+F(n-2)) end:

%p b:= proc(n) local j;

%p       if n=0 then 0

%p     else for j from 2 while F(j+1)<=n do od;

%p          b(n-F(j))+2^(j-2)

%p       fi

%p     end:

%p a:= n-> b(2^n):

%p seq(a(n), n=0..35);

%o (Python)

%o def A305876(n):

%o     m, tlist, s = 2**n, [1,2], 0

%o     while tlist[-1]+tlist[-2] <= m:

%o         tlist.append(tlist[-1]+tlist[-2])

%o     for d in tlist[::-1]:

%o         s *= 2

%o         if d <= m:

%o             s += 1

%o             m -= d

%o     return s # _Chai Wah Wu_, Jun 14 2018

%Y Cf. A000045, A000079, A003714 (Fibbinary), A007088, A014417, A305380.

%K nonn,base

%O 0,2

%A _Alois P. Heinz_, Jun 12 2018