A214852 -id:A214852 - cp's OEIS frontend

A259407 Fibonacci numbers corresponding to the indices mentioned in A214852.

2, 14930352, 267914296, 956722026041, 781774079430987230203437, 178890334785183168257455287891792, 57602132235424755886206198685365216, 55835073295300465536628086585786672357234389, 15156039800290547036315704478931467953361427680642

Offset: 1

Abhiram R Devesh, Jun 26 2015

The data correspond to the 3rd, 36th, 42nd, 59th, 116th, 156th, 168th, 211th, 237th Fibonacci numbers.

Intersection of A000045 and A031443. - Michel Marcus, Jul 31 2015

			a(2) = F(36) = 14930352 = 111000111101000110110000_2 has an equal number of 0's and 1's.

Paolo Xausa, Table of n, a(n) for n = 1..70

Cf. A000045, A031443, A214852.

Select[Fibonacci[Range[300]], Equal @@ DigitCount[#, 2] &] (* Paolo Xausa, Oct 31 2024 *)

f1=1; f2=1
while f1>0:
    f3=f1+f2
    c = bin(f3).split('b')[1]
    if c.count("1")==c.count("0"):
        print(f3)
    f1=f2; f2=f3

a(n) = A000045(A214852(n)).

A350700 a(n) is the number of 1's minus the number of 0's in A004685(n).

Original entry on oeis.org

-1, 1, 1, 0, 2, 1, -2, 2, 1, -2, 4, 1, -4, 2, 3, -2, 6, 3, -4, -3, 3, -2, 1, 7, -4, -5, 1, 4, 3, 5, -4, 1, -4, 4, 1, -2, 0, 3, -6, -2, 5, 6, 0, 3, 6, -1, 11, -6, -9, 3, 2, -1, -1, -2, -5, 6, 4, -7, 8, 0, -9, -4, 10, 3, -4, 6, -7, 6, -17, -1, -2, -5, 1, 4, -3

Offset: 0

Karl-Heinz Hofmann, Jan 18 2022

			A004685(0) = 0; this term has 0 ones and 1 zero. So a(0) = 0 - 1 = -1.
A004685(7) = 1101; this term has 3 ones and 1 zero. So a(7) = 3 - 1 = 2.

Karl-Heinz Hofmann, Table of n, a(n) for n = 0..10000

Cf. A000045, A004685, A011373, A145037, A177718, A214852.

a[n_] := Subtract @@ DigitCount[Fibonacci[n], 2, {1, 0}]; Array[a, 75, 0] (* Amiram Eldar, Jan 22 2022 *)

from sympy import fibonacci
print([(bin(fibonacci(n))[2:].count("1") - bin(fibonacci(n))[2:].count("0")) for n in range (0,100)])

a(n) = A145037(A000045(n)) for n >= 1.

a(n) = 0 if and only if n is in A214852. - Amiram Eldar, Jan 22 2022

cp's OEIS Frontend

A259407 Fibonacci numbers corresponding to the indices mentioned in A214852.

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