A328381 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.

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

Offset

1,1

Comments

No more terms below 1427.

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

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.

Links

Table of n, a(n) for n=1..14.

Example

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

Mathematica

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

Crossrefs

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

Supersequence of A281087.

Sequence in context: A004203 A201473 A088884 * A058029 A206640 A182354

Adjacent sequences: A328378 A328379 A328380 * A328382 A328383 A328384

Keyword

nonn,more

Author

Amiram Eldar, Oct 14 2019

Status

approved