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A290780
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Half-octavan primes: primes of the form (x^8 + y^8)/2.
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1
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198593, 21523361, 107182721, 407865361, 429388721, 3487882001, 11979660241, 39155495921, 84785726833, 141217650641, 141321947681, 250123401793, 253611085201, 289278699121, 391337974721, 426445714033, 426448401121
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OFFSET
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1,1
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LINKS
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EXAMPLE
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a(1) = (5^8 + 3^8)/2 = 198593.
a(2) = (9^8 + 1^8)/2 = 21523361.
a(3) = (11^8 + 3^8)/2 = 107182721.
a(4) = (13^8 + 1^8)/2 = 407865361.
a(5) = (13^8 + 9^8)/2 = 429388721.
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MAPLE
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N:= 10^12: # to get all terms <= N
sort(convert(select(isprime, {seq(seq((x^8+y^8)/2, y= (x mod 2)..min(x, floor((2*N-x^8)^(1/8))), 2), x=1..floor((2*N)^(1/8)))}), list)); # Robert Israel, Aug 21 2017
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MATHEMATICA
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Sort[Select[Total/@(Union[Sort/@Tuples[Range[0, 50], 2]]^8)/2, PrimeQ]] (* or *) lst={}; Do[If[PrimeQ[(a^8 + b^8) / 2], AppendTo[lst, (a^8 + b^8) / 2]], {a, 100}, {b, a, 100}]; Sort[lst] (* Vincenzo Librandi, Aug 21 2017 *)
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PROG
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(PARI) list(lim)=my(v=List(), x8, t); forstep(x=1, sqrtnint(lim\=1, 8), 2, x8=x^8; forstep(y=1, min(sqrtnint(lim-x8, 8), x-1), 2, if(isprime(t=(x8+y^8)/2), listput(v, t)))); Set(v) \\ Charles R Greathouse IV, Aug 20 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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STATUS
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approved
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