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

0,3

Comments

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

Links

Table of n, a(n) for n=0..70.

Example

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

Prog

(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),
  an = i = 0
  while res:
    if res&1:  an += fib[2+i]
    i += 1
    res >>= 1
  print an,

Crossrefs

Cf. A014417, A000045.

Sequence in context: A178151 A087794 A050514 * A335841 A133702 A328486

Adjacent sequences: A229044 A229045 A229046 * A229048 A229049 A229050

Keyword

nonn,base

Author

Alex Ratushnyak, Sep 25 2013

Status

approved