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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 for any kand F(a*b)= F(a) * F(b))). Thus the two squares are of consecutive Fibonacci numbers.

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proposed

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 for any k). Thus the two squares are of consecutive Fibonacci numbers.

No other terms up to FibonacciF(2904353).

Subsequence of A002144 and A002313.

FibonacciF(47) = 2971215073 = 28657^2 + 46368^2 = FibonacciF(23)^2 + FibonacciF(24)^2 and 2971215073 and 28657 are prime, so 2971215073 is a member.

Cf. A000045, A001605, A002144, A002313, A005478, A263467.

nonn,more,new

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editing

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editing

proposed

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 for any k).

Fibonacci(47) = 2971215073 = 28657^2 + 46368^2 = Fibonacci(23)^2 + Fibonacci(24)^2 and 2971215073 and 28657 are prime, so 2971215073 is a member.

allocated for Jonathan SondowFibonacci primes equal to a sum of squares of two Fibonacci numbers at least one of which is also prime.

5, 13, 89, 233, 28657, 2971215073

1,1

No other terms up to Fibonacci(2904353).

The corresponding Fibonacci indices are in A263467.

Wikipedia, <a href="https://en.wikipedia.org/wiki/Fibonacci_number">Fibonacci number</a>

Wikipedia, <a href="https://en.wikipedia.org/wiki/Fibonacci_prime">Fibonacci prime</a>

a(n) = A000045(A263467(n)).

Fibonacci(47) = 2971215073 = 28657^2 + 46368^2 = Fibonacci(23)^2 + Fibonacci(24)^2 and 2971215073 and 28657 are prime, so 2971215073 is a member.

Cf. A000045, A001605, A005478, A263467.

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Jonathan Sondow, Nov 04 2015

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allocated for Jonathan Sondow

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