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A214852 Indices of Fibonacci numbers with the same number of 1's and 0's in their binary representation. 3
3, 36, 42, 59, 116, 156, 168, 211, 237, 246, 280, 335, 355, 399, 404, 416, 433, 442, 569, 580, 652, 698, 761, 770, 865, 897, 940, 989, 1041, 1049, 1101, 1144, 1214, 1286, 1335, 1352, 1369, 1395, 1698, 1726, 1810, 1928, 1940, 1951, 2055, 2159, 2326, 2332 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Conjecture: the sequence is infinite.

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

LINKS

T. D. Noe, Table of n, a(n) for n = 1..400

EXAMPLE

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

MATHEMATICA

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

PROG

(Python)

def count10(x):

c0, c1, m = 0, 0, 1

while m<=x:

if x&m:

c1+=1

else:

c0+=1

m+=m

return c0-c1

prpr, prev = 0, 1

TOP = 1<<16

for i in range(1, TOP):

if count10(prev)==0:

print i,

prpr, prev = prev, prpr+prev

CROSSREFS

Cf. A000045, A004685, A259407.

Sequence in context: A291213 A158301 A105758 * A113799 A072682 A158207

Adjacent sequences: A214849 A214850 A214851 * A214853 A214854 A214855

KEYWORD

nonn,base

AUTHOR

Alex Ratushnyak, Mar 08 2013

STATUS

approved

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Last modified December 4 19:07 EST 2022. Contains 358563 sequences. (Running on oeis4.)