A214852 - OEIS

%I #26 Jan 22 2022 18:20:28

%S 3,36,42,59,116,156,168,211,237,246,280,335,355,399,404,416,433,442,

%T 569,580,652,698,761,770,865,897,940,989,1041,1049,1101,1144,1214,

%U 1286,1335,1352,1369,1395,1698,1726,1810,1928,1940,1951,2055,2159,2326,2332

%N Indices of Fibonacci numbers with the same number of 1's and 0's in their binary representation.

%C Conjecture: the sequence is infinite.

%C The sequence of Fibonacci numbers with the same number of 1's and 0's in their binary representation begins: 2, 14930352, 267914296, ... = A259407.

%H T. D. Noe, <a href="/A214852/b214852.txt">Table of n, a(n) for n = 1..400</a>

%e Fibonacci(36) = 14930352 = 111000111101000110110000_2, twelve 1's and twelve 0's, therefore 36 is in the sequence.

%t fQ[n_] := Module[{f = IntegerDigits[Fibonacci[n], 2]}, Count[f, 0] == Count[f, 1]]; Select[Range[3000], fQ] (* _T. D. Noe_, Mar 08 2013 *)

%o (Python)

%o def count10(x):

%o     c0, c1, m = 0, 0, 1

%o     while m<=x:

%o       if x&m:

%o         c1+=1

%o       else:

%o         c0+=1

%o       m+=m

%o     return c0-c1

%o prpr, prev = 0,1

%o TOP = 1<<16

%o for i in range(1,TOP):

%o     if count10(prev)==0:

%o         print i,

%o     prpr, prev = prev, prpr+prev

%Y Cf. A000045, A004685, A259407.

%K nonn,base

%O 1,1

%A _Alex Ratushnyak_, Mar 08 2013