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A272170 Second most significant bit of Fibonacci numbers > 1 written in base 2. 8
0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 1, 0, 1, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 1, 0, 1, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 1, 0, 1, 1, 0, 0, 1, 0 (list; graph; refs; listen; history; text; internal format)
OFFSET
3,1
COMMENTS
It is conjectured that there are no more than two consecutive "0's" or “1’s” (tested up to n=10^5). The sequence looks quasiperiodic and its Fourier spectrum seems to have a fractal structure.
LINKS
FORMULA
a(n) = floor(A000045(n)/(2^(ceiling(log_2(A000045(n) + 1)) - 2))) - 2.
a(n) = A079944(A000045(n)-2). - Michel Marcus, Apr 22 2016
EXAMPLE
(second MSB in parenthesis)
n A000045(n) A004685(n)
3 2 -> 1(0)
4 3 -> 1(1)
5 5 -> 1(0)1
6 8 -> 1(0)00
7 13 -> 1(1)01
8 21 -> 1(0)101
9 34 -> 1(0)0010
10 55 -> 1(1)0111
...
MATHEMATICA
nmax = 120; Table[IntegerDigits[Fibonacci[j], 2][[2]], {j, 3, nmax}]
PROG
(PARI) a(n) = binary(fibonacci(n))[2]; \\ Michel Marcus, Apr 25 2016
(Python)
A272170_list, a, b = [], 1 , 1
for n in range(3, 10001):
a, b = b, a+b
A272170_list.append(int(bin(b)[3])) # Chai Wah Wu, Feb 07 2018
CROSSREFS
Sequence in context: A163584 A353307 A286655 * A126565 A215531 A305386
KEYWORD
nonn,base
AUTHOR
Andres Cicuttin, Apr 21 2016
STATUS
approved

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Last modified April 25 09:20 EDT 2024. Contains 371967 sequences. (Running on oeis4.)