login
A305876
a(n) = Fibbinary(2^n).
2
1, 2, 5, 16, 36, 84, 273, 648, 2114, 4757, 16516, 37161, 87045, 282896, 673924, 2184233, 5263877, 17107472, 38830244, 134554132, 303080705, 707272770, 2300725397, 5457925252, 17805431433, 42970665029, 139654661284, 314223120404, 1099646108737, 2474203744786
OFFSET
0,2
LINKS
FORMULA
a(n) = A003714(2^n).
A014417(2^n) = A007088(a(n)).
EXAMPLE
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).
MAPLE
F:= proc(n) F(n):= `if`(n<2, n, F(n-1)+F(n-2)) end:
b:= proc(n) local j;
if n=0 then 0
else for j from 2 while F(j+1)<=n do od;
b(n-F(j))+2^(j-2)
fi
end:
a:= n-> b(2^n):
seq(a(n), n=0..35);
PROG
(Python)
def A305876(n):
m, tlist, s = 2**n, [1, 2], 0
while tlist[-1]+tlist[-2] <= m:
tlist.append(tlist[-1]+tlist[-2])
for d in tlist[::-1]:
s *= 2
if d <= m:
s += 1
m -= d
return s # Chai Wah Wu, Jun 14 2018
CROSSREFS
Sequence in context: A174988 A364706 A053683 * A082085 A179992 A054971
KEYWORD
nonn,base
AUTHOR
Alois P. Heinz, Jun 12 2018
STATUS
approved