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A096170
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Primes of the form (n^4 + 1)/2.
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3
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41, 313, 1201, 7321, 14281, 41761, 97241, 139921, 353641, 750313, 1156721, 5278001, 6922921, 8925313, 12705841, 14199121, 21523361, 56275441, 60775313, 81523681, 87450313, 100266961, 138461441, 273990641, 370600313, 407865361
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OFFSET
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1,1
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COMMENTS
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Note that n must be odd. Terms of primitive Pythagorean triples: (n^2, (n^4-1)/2, (n^4+1)/2).
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LINKS
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EXAMPLE
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a(1)=41 because (3^4 + 1)/2 = 82/2 = 41 is prime.
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MATHEMATICA
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PROG
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(Magma) [ a: n in [0..2500] | IsPrime(a) where a is ((n^4+1) div 2) ]; // Vincenzo Librandi, Apr 15 2011
(PARI) list(lim)=my(v=List(), t); forstep(n=3, sqrtnint(lim\1*2-1, 4), 2, if(isprime(t=(n^4+1)/2), listput(v, t))); Vec(v) \\ Charles R Greathouse IV, Feb 14 2017
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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