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A272170 Second most significant bit of Fibonacci numbers > 1 written in base 2. 6
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 ā€œ1ā€™sā€ (tested up to n=10^5). The sequence looks quasiperiodic and its Fourier spectrum seems to have a fractal structure.

LINKS

Chai Wah Wu, Table of n, a(n) for n = 3..10000

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

Cf. A000045, A004685, A079944, A271591.

Sequence in context: A175253 A163584 A286655 * A126565 A215531 A305386

Adjacent sequences:  A272167 A272168 A272169 * A272171 A272172 A272173

KEYWORD

nonn,base

AUTHOR

Andres Cicuttin, Apr 21 2016

STATUS

approved

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Last modified March 23 16:52 EDT 2019. Contains 321432 sequences. (Running on oeis4.)