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A263468 Fibonacci primes equal to a sum of squares of two Fibonacci numbers at least one of which is also prime. 1
5, 13, 89, 233, 28657, 2971215073 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
COMMENTS
Same as Fibonacci numbers F(2k+1) such that at least two of the numbers F(2k+1), F(k), F(k+1) are prime (because F(2k+1) = F(k)^2 + F(k+1)^2 and F(a*b)= F(a) * F(b))). Thus the two squares are of consecutive Fibonacci numbers.
No other terms up to F(2904353).
The corresponding Fibonacci indices are in A263467.
Subsequence of A002144 and A002313.
LINKS
Wikipedia, Fibonacci number
Wikipedia, Fibonacci prime
FORMULA
a(n) = A000045(A263467(n)).
EXAMPLE
F(47) = 2971215073 = 28657^2 + 46368^2 = F(23)^2 + F(24)^2 and 2971215073 and 28657 are prime, so 2971215073 is a member.
CROSSREFS
Sequence in context: A165262 A092955 A190949 * A350467 A081560 A057624
KEYWORD
nonn,more
AUTHOR
Jonathan Sondow, Nov 04 2015
STATUS
approved

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Last modified April 15 00:51 EDT 2024. Contains 371667 sequences. (Running on oeis4.)