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%I #17 Dec 11 2015 14:04:13
%S 1,2,19,31,37,38,41,53,59,61,62,67,71,73,74,79,82,89,97,101,103,106,
%T 107,109,113,118,122,127,134,139,142,146,149,151,157,158,163,167,173,
%U 178,179,181,191,193,194,197,199,202,206,211,214,218,223,226,227,229,233,239,241,251,254,257
%N Numbers n such that the n-th Fibonacci number is not divisible by any prime Fibonacci number.
%C n is in this sequence if and only if it is not divisible by any member of A001605.
%C Conjecture: this sequence has natural density around 0.229. (The sequence has a natural density unless Fibonacci primes are much denser than expected.)
%C 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
%H Charles R Greathouse IV, <a href="/A261312/b261312.txt">Table of n, a(n) for n = 1..10000</a>
%e The 19th Fibonacci is 4181 = 37*113, but neither 37 nor 113 is a Fibonacci number so 19 is in this sequence.
%o (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
%Y Cf. A000045, A001605, A090819.
%K nonn
%O 1,2
%A _Charles R Greathouse IV_, Aug 14 2015
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