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A290780 Half-octavan primes: primes of the form (x^8 + y^8)/2. 1
198593, 21523361, 107182721, 407865361, 429388721, 3487882001, 11979660241, 39155495921, 84785726833, 141217650641, 141321947681, 250123401793, 253611085201, 289278699121, 391337974721, 426445714033, 426448401121 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

LINKS

Charles R Greathouse IV, Table of n, a(n) for n = 1..10000

A. J. C. Cunningham, High quartan factorisations and primes, Messenger of Mathematics 36 (1907), pp. 145-174.

EXAMPLE

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.

MAPLE

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

MATHEMATICA

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 *)

PROG

(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

CROSSREFS

Cf. A006686, A002646.

Sequence in context: A215996 A205234 A249358 * A255782 A205638 A031687

Adjacent sequences:  A290777 A290778 A290779 * A290781 A290782 A290783

KEYWORD

nonn

AUTHOR

Charles R Greathouse IV, Aug 20 2017

STATUS

approved

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Last modified February 19 09:33 EST 2020. Contains 332041 sequences. (Running on oeis4.)