A180280 Fibonacci numbers written in base 2, read as decimal numbers which then are prime.

11, 101, 1011001, 100010100101111, 1100110010100000101000011101110110101011001011001101111101101011010101110010101, 1101011110011100100011101000011100001010001101001011001100110100000011001101101001010011011001100101010111

Offset

1,1

Comments

Subset of A020449 (Primes that contain digits 0 and 1 only).

Generated by A000045(k), k= 4, 5, 11, 22, 115, 154,... [R. J. Mathar, Aug 26 2010]

No further terms through the 5,000th Fibonacci number, which has 3,471 digits in base 2. - Harvey P. Dale, Sep 04 2024

Links

Table of n, a(n) for n=1..6.

Formula

Primes in A004685. Primes in {A007088(A000045(n))}.

Example

a(1) = 11 because 3 is the 4th Fibonacci number, 3 (base 2) = 11, and 11 (base 10) is prime.
a(2) = 101 because 5 is the 5th Fibonacci number, 5 (base 2) = 101, and 101 (base 10) is prime.
a(3) = 1011001 because 89 is the 11th Fibonacci number, 89 (base 2) = 1011001, and 1011001 (base 10) is prime.
a(4) = 100010100101111 because 17711 is the 22nd Fibonacci number, 17711 (base 2) = 100010100101111, and 100010100101111 (base 10) is prime.

Mathematica

Select[FromDigits[IntegerDigits[#, 2]]&/@Fibonacci[Range[1000]], PrimeQ] (* Harvey P. Dale, Sep 04 2024 *)

Crossrefs

Cf. A000040, A000045, A004685, A005478, A007088, A020449.

Sequence in context: A001387 A358198 A247863 * A100580 A253631 A087744

Adjacent sequences: A180277 A180278 A180279 * A180281 A180282 A180283

Keyword

nonn,base,less

Author

Jonathan Vos Post, Aug 24 2010

Extensions

Two more terms from R. J. Mathar, Aug 26 2010

Status

approved