A004686 -id:A004686 - cp's OEIS frontend

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

N. J. A. Sloane

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).

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.

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

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

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

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

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

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

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

A030363 Write (n+1)st Fibonacci number in base 3 and juxtapose.

Original entry on oeis.org

1, 2, 1, 0, 1, 2, 2, 2, 1, 1, 1, 2, 1, 0, 1, 0, 2, 1, 2, 0, 0, 1, 1, 0, 0, 2, 2, 1, 2, 1, 0, 0, 2, 2, 1, 2, 2, 1, 1, 1, 2, 2, 2, 2, 1, 1, 1, 2, 1, 1, 1, 0, 0, 1, 2, 0, 2, 0, 1, 2, 0, 1, 1, 1, 0, 1, 1, 2, 2, 0, 1, 1, 2, 2, 0, 1, 2, 1, 2, 1, 0, 0, 0, 2, 1, 1, 2, 0, 1, 2

Offset: 1

Clark Kimberling

Cf. A004686 (Fibonacci numbers written in base 3).

Flatten[IntegerDigits[Fibonacci[Range[2,30]],3]] (* Harvey P. Dale, Apr 09 2015 *)

A214326 Square array read by antidiagonals in which T(n,b) gives the n-th Fibonacci number written in base b with n,b >= 1.

Original entry on oeis.org

1, 1, 1, 1, 1, 11, 1, 1, 10, 111, 1, 1, 2, 11, 11111, 1, 1, 2, 10, 101, 11111111, 1, 1, 2, 3, 12, 1000, 1111111111111, 1, 1, 2, 3, 11, 22, 1101, 111111111111111111111, 1, 1, 2, 3, 10, 20, 111, 10101, 1111111111111111111111111111111111, 1, 1, 2, 3, 5, 13, 31, 210, 100010

Offset: 1

Alois P. Heinz, Jul 24 2012

For b > 10, some terms cannot be properly notated using only decimal characters.

			Square array A(n,b) begins:
              1,    1,   1,  1,  1,  1,  1,  1,  1,  1,  1,  1, ...
              1,    1,   1,  1,  1,  1,  1,  1,  1,  1,  1,  1, ...
             11,   10,   2,  2,  2,  2,  2,  2,  2,  2,  2,  2, ...
            111,   11,  10,  3,  3,  3,  3,  3,  3,  3,  3,  3, ...
          11111,  101,  12, 11, 10,  5,  5,  5,  5,  5,  5,  5, ...
       11111111, 1000,  22, 20, 13, 12, 11, 10,  8,  8,  8,  8, ...
  1111111111111, 1101, 111, 31, 23, 21, 16, 15, 14, 13, 12, 11, ...

Alois P. Heinz, Antidiagonals n = 1..13

Columns b=1-10, 12, 13 give: A108047, A004685, A004686, A004687, A004688, A004689, A004690, A004691, A004692, A000045, A004693, A004694.

Cf. A037842, A131293.

A:= proc(n, b) local f, l; f:= combinat[fibonacci](n);
      if b=1 then parse(cat(1$f))
    else l:= NULL;
         while f>0 do l:= irem(f, b, 'f'), l od;
         parse(cat(l))
      fi
    end:
seq(seq(A(n, 1+d-n), n=1..d), d=1..10);

A111064 Numbers n such that the sum of the digits of the n-th Fibonacci number written in bases 2, 3, 5 and 7 is prime.

Original entry on oeis.org

7, 8, 10, 17, 47, 61, 70, 170, 185, 299, 766, 950, 1247, 1669, 1879, 2063, 2090, 2701, 3071, 5809, 6190, 7057, 7409, 8410, 12754, 13303, 13421, 14533, 16250, 18793, 24766, 24895, 27370, 28594, 28870, 29093, 29189, 30647, 31481, 36334, 38123, 38957

Offset: 1

Stefan Steinerberger, Nov 12 2005

			21 is the 8th Fibonacci number. Written in bases 2,3,5,7 we obtain 10101, 210, 41 and 30. The sum of the digits of each of this representations is prime, so 8 is an element of the sequence.

Cf. A004685, A004686, A004688, A004690.

fQ[n_] := Union@PrimeQ[Plus @@@ IntegerDigits[ Fibonacci@n, {2, 3, 5, 7}]] == {True}; Select[ Range[39285], fQ[ # ] &] (* Robert G. Wilson v *)
Select[Range[40000],AllTrue[Total/@IntegerDigits[Fibonacci[#],{2,3,5,7}],PrimeQ]&] (* Harvey P. Dale, Sep 09 2021 *)

for n from 1 to 1500 do a := numlib::fibonacci(n); if numlib::proveprime(numlib::sumOfDigits(a,2)) = TRUE then if numlib::proveprime(numlib::sumOfDigits(a,3)) = TRUE then if numlib::proveprime(numlib::sumOfDigits(a,5)) = TRUE then if numlib::proveprime(numlib::sumOfDigits(a,7)) = TRUE then print(n); end_if; end_if; end_if; end_if; end_for;

More terms from Robert G. Wilson v, Nov 14 2005

Corrected by Harvey P. Dale, Sep 09 2021

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A004685 Fibonacci numbers written in base 2.

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A030363 Write (n+1)st Fibonacci number in base 3 and juxtapose.

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A214326 Square array read by antidiagonals in which T(n,b) gives the n-th Fibonacci number written in base b with n,b >= 1.

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A111064 Numbers n such that the sum of the digits of the n-th Fibonacci number written in bases 2, 3, 5 and 7 is prime.

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