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A214852 Indices of Fibonacci numbers with the same number of 1's and 0's in their binary representation. 2
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, 956722026041, 781774079430987230203437, 178890334785183168257455287891792, 57602132235424755886206198685365216, 55835073295300465536628086585786672357234389

LINKS

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

EXAMPLE

Fibonacci(36)=14930352 is 111000111101000110110000 in binary, 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.

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 April 18 22:08 EDT 2019. Contains 322237 sequences. (Running on oeis4.)