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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 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

LINKS

Alois P. Heinz, Table of n, a(n) for n = 0..2306

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

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

Sequence in context: A196025 A174988 A053683 * A082085 A179992 A054971

Adjacent sequences:  A305873 A305874 A305875 * A305877 A305878 A305879

KEYWORD

nonn,base

AUTHOR

Alois P. Heinz, Jun 12 2018

STATUS

approved

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Last modified April 5 10:28 EDT 2020. Contains 333239 sequences. (Running on oeis4.)