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A291944
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a(n) is the least A for which there exists B with 0 < B < A so that A^(2^n) + B^(2^n) is prime.
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5
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2, 2, 2, 2, 2, 9, 11, 27, 14, 13, 47, 22, 53, 72, 216, 260, 124, 1196, 200
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OFFSET
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0,1
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COMMENTS
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A^(2^n) + B^(2^n) is called an (extended) generalized Fermat prime, and often denoted F_n(A, B); or xGF(n, A, B).
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LINKS
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EXAMPLE
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a(10)=47 corresponds to the prime number 47^1024 + 26^1024, the smallest prime number of the form A^1024 + B^1024 (or more precisely, it minimizes A).
a(14)=216 corresponds to the prime number 216^16384 + 109^16384, a 38248-decimal digit PRP, the smallest prime number of the form A^16384 + B^16384. - Serge Batalov, Mar 16 2018
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MATHEMATICA
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f[n_] := Monitor[ Block[{a = 2, b}, While[a < Infinity, b = 1 +Mod[a, 2]; While[b < a, If[ PrimeQ[a^2^n + b^2^n], Goto[fini]]; b+=2]; a++]; Label[fini]; {a, b}], {a, b}]; Array[f, 14, 0] (* Robert G. Wilson v, Mar 10 2018 *)
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PROG
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(PARI) for(n=0, 30, for(a=2, 10^100, forstep(b=(a % 2)+1, a-1, 2, if(ispseudoprime(a^(2^n)+b^(2^n)), print1(a, ", "); next(3)))))
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CROSSREFS
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KEYWORD
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nonn,hard,more
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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