STATUS
proposed
approved
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Revision History for A328381
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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.
(history; published version)
(history; published version)
STATUS
editing
proposed
NAME
allocated for Amiram EldarLesser 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.
DATA
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.
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
KEYWORD
allocated
nonn,more
AUTHOR
Amiram Eldar, Oct 14 2019
STATUS
approved
editing
NAME
allocated for Amiram Eldar
KEYWORD
allocated
STATUS
approved