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Fibonacci numbers F that are squarefree semiprimes such that F+2 or F-2 is also a squarefree semiprime.
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%I #15 Aug 02 2024 01:55:58

%S 55,4181,17711,121393,5702887

%N Fibonacci numbers F that are squarefree semiprimes such that F+2 or F-2 is also a squarefree semiprime.

%C a(6) > Fibonacci(1500), if it exists. - _Amiram Eldar_, Aug 01 2024

%e 55 = Fibonacci(10) is a term because 55 = 5 * 11 and 55 + 2 = 57 = 3 * 19 are both squarefree semiprimes.

%e 4181 = Fibonacci(19) is a term because 4181 = 37 * 113 and 4181 + 2 = 4183 = 47 * 89 are both squarefree semiprimes.

%t Select[Fibonacci[Range[300]], Last/@FactorInteger[#]=={1,1} && (Last/@FactorInteger[#+2]=={1,1} || Last/@FactorInteger[#-2]=={1,1})&]

%Y Subsequence of A000045, A006881 and A053409.

%Y Cf. A072381.

%K nonn

%O 1,1

%A _Vladimir Joseph Stephan Orlovsky_, Feb 03 2012

%E Name corrected by _Amiram Eldar_, Aug 01 2024