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A206097
Fibonacci numbers F that are squarefree semiprimes such that F+2 or F-2 is also a squarefree semiprime.
0
55, 4181, 17711, 121393, 5702887
OFFSET
1,1
COMMENTS
a(6) > Fibonacci(1500), if it exists. - Amiram Eldar, Aug 01 2024
EXAMPLE
55 = Fibonacci(10) is a term because 55 = 5 * 11 and 55 + 2 = 57 = 3 * 19 are both squarefree semiprimes.
4181 = Fibonacci(19) is a term because 4181 = 37 * 113 and 4181 + 2 = 4183 = 47 * 89 are both squarefree semiprimes.
MATHEMATICA
Select[Fibonacci[Range[300]], Last/@FactorInteger[#]=={1, 1} && (Last/@FactorInteger[#+2]=={1, 1} || Last/@FactorInteger[#-2]=={1, 1})&]
CROSSREFS
Subsequence of A000045, A006881 and A053409.
Cf. A072381.
Sequence in context: A060077 A035323 A250833 * A103918 A013537 A056567
KEYWORD
nonn
AUTHOR
EXTENSIONS
Name corrected by Amiram Eldar, Aug 01 2024
STATUS
approved