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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).

%I A229047 #31 Oct 16 2024 14:53:00
%S A229047 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,
%T A229047 33,32,33,54,88,13,14,15,25,16,17,28,46,18,19,20,33,32,33,54,88,29,30,
%U A229047 31,51,32,33,54,88,52,53,54,88,87,88,143,232,21,22,23,38,24,25,41
%N 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).
%C A229047 Index of r in A014417, where r = ReplaceAll('11' -> '101' in bin(n)).
%e A229047 Base 2 representation of 14 is 1110, that is 101010 after the replacement, that is A014417(20), so a(14)=20.
%o A229047 (Python)
%o A229047 fib = [0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610, 987, 1597]
%o A229047 for n in range(333):
%o A229047   res = 0
%o A229047   bit = resbit = 1
%o A229047   while bit<=n:
%o A229047     if n&bit:  res += resbit
%o A229047     resbit*=2
%o A229047     if (n&bit) and (n&(bit*2)):  resbit*=2
%o A229047     bit*=2
%o A229047   #print(bin(n), bin(res), end=', ')
%o A229047   an = i = 0
%o A229047   while res:
%o A229047     if res&1:  an += fib[2+i]
%o A229047     i += 1
%o A229047     res >>= 1
%o A229047   print(an, end=', ')
%Y A229047 Cf. A014417, A000045.
%K A229047 nonn,base
%O A229047 0,3
%A A229047 _Alex Ratushnyak_, Sep 25 2013