A004685 Fibonacci numbers written in base 2.

0, 1, 1, 10, 11, 101, 1000, 1101, 10101, 100010, 110111, 1011001, 10010000, 11101001, 101111001, 1001100010, 1111011011, 11000111101, 101000011000, 1000001010101, 1101001101101, 10101011000010, 100010100101111, 110111111110001, 1011010100100000, 10010010100010001

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn
• easy
• base

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..1000
• Wayne State University College of Engineering, Engineering Bits & Bytes: The Fibonacci Puzzle, (Video, this sequence is looped through in 16-bit words close to the beginning and again at the end).

Crossrefs

Cf. A004686 .. A004694: Fibonacci numbers written in base 3, 4, ..., 13.

Cf. A004676 .. A004684: Primes written in base 2, 3, 4, ..., 11.

Cf. A004643, ..., A004668 : powers of 2 resp. of 3 in base 3, 4, 5, ..., 26.

Programs

Magma

[Seqint(Intseq(Fibonacci(n),2)): n in [0..50]]; // G. C. Greubel, Oct 09 2018

Maple

with(combinat): seq(convert(fibonacci(n),binary),n=0..25); # Muniru A Asiru, Oct 10 2018

Mathematica

Table[FromDigits[IntegerDigits[Fibonacci[n], 2]], {n, 0, 30}] (* Stefan Steinerberger, Apr 14 2006 *)

PARI

a(n)=subst(Pol(binary(fibonacci(n))),'x,10) \\ Charles R Greathouse IV, Feb 03 2014

PARI

apply( n->fromdigits(binary(fibonacci(n))), [0..19]) \\ M. F. Hasler, Jun 22 2018

PARI

vector(50, n, n--; fromdigits(digits(fibonacci(n), 2))) \\ G. C. Greubel, Oct 09 2018

Formula

a(n) = A007088(A000045(n)). - Jonathan Vos Post, Aug 24 2010