A229047 Replace all '11' => '101' in the binary representation of n, treat the result as representation of a(n) in base of Fibonacci numbers (A014417).

0, 1, 2, 4, 3, 4, 7, 12, 5, 6, 7, 12, 11, 12, 20, 33, 8, 9, 10, 17, 11, 12, 20, 33, 18, 19, 20, 33, 32, 33, 54, 88, 13, 14, 15, 25, 16, 17, 28, 46, 18, 19, 20, 33, 32, 33, 54, 88, 29, 30, 31, 51, 32, 33, 54, 88, 52, 53, 54, 88, 87, 88, 143, 232, 21, 22, 23, 38, 24, 25, 41

Offset: 0

Author

Alex Ratushnyak, Sep 25 2013

Keywords

• nonn
• base

Comments

Index of r in A014417, where r = ReplaceAll('11' -> '101' in bin(n)).

Examples

			Base 2 representation of 14 is 1110, that is 101010 after the replacement, that is A014417(20), so a(14)=20.
		

Crossrefs

Cf. A014417, A000045.

Programs

Python

fib = [0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610, 987, 1597]
for n in range(333):
  res = 0
  bit = resbit = 1
  while bit<=n:
    if n&bit:  res += resbit
    resbit*=2
    if (n&bit) and (n&(bit*2)):  resbit*=2
    bit*=2
  #print(bin(n), bin(res), end=', ')
  an = i = 0
  while res:
    if res&1:  an += fib[2+i]
    i += 1
    res >>= 1
  print(an, end=', ')