A328381 - OEIS

%I #4 Oct 14 2019 21:13:32

%S 3,5,11,59,71,107,179,191,311,431,569,599,827,881

%N Lesser of twin primes pair p, such that F(p) and F(p+2) have the same number of prime factors, where F(n) is the n-th Fibonacci number.

%C No more terms below 1427.

%C The corresponding number of prime factors is 1, 1, 1, 2, 2, 2, 3, 2, 4, 1, 1, 2, 5, ...

%C Assuming that Fibonacci numbers with prime index are always squarefree, the distinction between number of prime factors with multiplicity (A001222) and number of distinct prime factors (A001221) is inessential.

%e 3 is in the sequence since 3 and 5 are twin primes, and F(3) = 2 and F(5) = 5 are both primes, thus having the same number of prime factors.

%e 71 is in the sequence since 71 and 73 are twin primes, and F(71) and F(73) both have 2 prime factors.

%t s={}; Do[If[PrimeQ[n] && PrimeQ[n+2] && PrimeOmega[Fibonacci[n]] == PrimeOmega[ Fibonacci[n+2]], AppendTo[s, n]], {n, 1, 200}]; s

%Y Cf. A000045, A001359, A001605, A005478, A022307, A038575, A319908.

%Y Supersequence of A281087.

%K nonn,more

%O 1,1

%A _Amiram Eldar_, Oct 14 2019