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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 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: A163584 A353307 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 April 25 09:20 EDT 2024. Contains 371967 sequences. (Running on oeis4.)