A261312 Numbers n such that the n-th Fibonacci number is not divisible by any prime Fibonacci number.

1, 2, 19, 31, 37, 38, 41, 53, 59, 61, 62, 67, 71, 73, 74, 79, 82, 89, 97, 101, 103, 106, 107, 109, 113, 118, 122, 127, 134, 139, 142, 146, 149, 151, 157, 158, 163, 167, 173, 178, 179, 181, 191, 193, 194, 197, 199, 202, 206, 211, 214, 218, 223, 226, 227, 229, 233, 239, 241, 251, 254, 257

Offset: 1

Author

Charles R Greathouse IV, Aug 14 2015

Keywords

• nonn

Comments

n is in this sequence if and only if it is not divisible by any member of A001605.

Conjecture: this sequence has natural density around 0.229. (The sequence has a natural density unless Fibonacci primes are much denser than expected.)

There are 232 terms up to 10^3, 2293 terms up to 10^4, 22869 terms up to 10^5, and 228896 terms up to 10^6. - Charles R Greathouse IV, Dec 11 2015

Examples

			The 19th Fibonacci is 4181 = 37*113, but neither 37 nor 113 is a Fibonacci number so 19 is in this sequence.
		

Links

• Charles R Greathouse IV, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A000045, A001605, A090819.

Programs

PARI

is(n)=if(gcd(1155,n)>1||n%4==0, return(0)); my(f=factor(n)[,1]); for(i=1,#f, if(ispseudoprime(fibonacci(f[i])), return(0))); 1