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

11, 101, 1011001, 100010100101111, 1100110010100000101000011101110110101011001011001101111101101011010101110010101, 1101011110011100100011101000011100001010001101001011001100110100000011001101101001010011011001100101010111

Offset: 1

Author

Jonathan Vos Post, Aug 24 2010

Keywords

• nonn
• base
• less

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

Examples

			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.
		

Crossrefs

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

Programs

Mathematica

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

Formula

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

Extensions

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