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A343121
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a(n) is the least A for which there exists B with 0 < B < A so that A^(2^k) + B^(2^k) is prime for k = 0, 1, ..., n.
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0
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OFFSET
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0,1
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COMMENTS
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For n < 5, the corresponding primes are Fermat primes, for higher n so-called generalized Fermat primes.
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LINKS
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Yves Gallot, xgfp8, software for calculating this sequence.
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EXAMPLE
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For n=5, the six numbers 2669 + 720, 2669^2 + 720^2, 2669^4 + 720^4, 2669^8 + 720^8, 2669^16 + 720^16, and 2669^32 + 720^32 are all prime, and (A,B) = (2669,720) is the least pair with this property, so a(5)=2669.
For n=6, (A,B) = (34559,29000).
For n=7, (A,B) = (26507494,6329559).
For n=8, (A,B) = (3242781025,1554825312).
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PROG
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(PARI) a(n)=for(A=1, oo, for(B=1, A-1, for(k=0, n, !ispseudoprime(A^(2^k)+B^(2^k)) && next(2)); return(A)))
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CROSSREFS
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KEYWORD
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nonn,more,hard
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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