login
The OEIS is supported by the many generous donors to the OEIS Foundation.

 

Logo

Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 59th year, we have over 358,000 sequences, and we’ve crossed 10,300 citations (which often say “discovered thanks to the OEIS”).

Other ways to Give
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A337923 a(n) is the exponent of the highest power of 2 dividing the n-th Fibonacci number. 2
0, 0, 1, 0, 0, 3, 0, 0, 1, 0, 0, 4, 0, 0, 1, 0, 0, 3, 0, 0, 1, 0, 0, 5, 0, 0, 1, 0, 0, 3, 0, 0, 1, 0, 0, 4, 0, 0, 1, 0, 0, 3, 0, 0, 1, 0, 0, 6, 0, 0, 1, 0, 0, 3, 0, 0, 1, 0, 0, 4, 0, 0, 1, 0, 0, 3, 0, 0, 1, 0, 0, 5, 0, 0, 1, 0, 0, 3, 0, 0, 1, 0, 0, 4, 0, 0, 1 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,6

LINKS

Amiram Eldar, Table of n, a(n) for n = 1..10000

Tamás Lengyel, The order of the Fibonacci and Lucas numbers, The Fibonacci Quarterly, Vol. 33, No. 3 (1995), pp. 234-239.

FORMULA

a(n) = A007814(A000045(n)).

The following 4 formulas completely specify the sequence (Lengyel, 1995):

1. a(n) = 0 if n == 1 (mod 3) or n == 2 (mod 3).

2. a(n) = 1 if n == 3 (mod 6).

3. a(n) = 3 if n == 6 (mod 12).

4. a(n) = A007814(n) + 2 if n == 0 (mod 12).

a(A001651(n)) = 0.

a(A016945(n)) = 1.

a(A017593(n)) = 3.

a(A073762(n)) = 4.

The image of this function is A184985, i.e., all the nonnegative integers excluding 2.

Asymptotic mean: lim_{n->oo} (1/n) * Sum_{k=1..n} a(k) = 5/6.

EXAMPLE

a(1) = 0 since Fibonacci(1) = 1 is odd.

a(6) = 3 since Fibonacci(6) = 8 = 2^3.

a(12) = 4 since Fibonacci(12) = 144 = 2^4 * 3^2.

MATHEMATICA

a[n_] := IntegerExponent[Fibonacci[n], 2]; Array[a, 100]

PROG

(Python)

def A337923(n): return int(not n%3)+(int(not n%6)<<1) if n%12 else 2+(~n&n-1).bit_length() # Chai Wah Wu, Jul 10 2022

CROSSREFS

Cf. A000045, A007814, A248174.

Cf. A001651, A016945, A017593, A073762, A184985.

Sequence in context: A167163 A005890 A104515 * A324874 A324862 A324864

Adjacent sequences: A337920 A337921 A337922 * A337924 A337925 A337926

KEYWORD

nonn

AUTHOR

Amiram Eldar, Jan 29 2021

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified December 8 20:46 EST 2022. Contains 358698 sequences. (Running on oeis4.)