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A261312 Numbers n such that the n-th Fibonacci number is not divisible by any prime Fibonacci number. 1
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

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

LINKS

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

EXAMPLE

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

PROG

(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

CROSSREFS

Cf. A000045, A001605, A090819.

Sequence in context: A284496 A120276 A006962 * A090819 A254897 A059697

Adjacent sequences:  A261309 A261310 A261311 * A261313 A261314 A261315

KEYWORD

nonn

AUTHOR

Charles R Greathouse IV, Aug 14 2015

STATUS

approved

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Last modified May 11 21:35 EDT 2021. Contains 343808 sequences. (Running on oeis4.)