A283019 Primes which are the sum of three nonzero 8th powers.

3, 6563, 72353, 137633, 787811, 1745153, 7444673, 44726593, 49202147, 61503553, 86093443, 91858243, 100006817, 100072097, 101686177, 107444417, 143046977, 200006561, 214756067, 257412163, 300452323, 430372577, 431661313, 435812033, 447149537, 452523713, 489805633, 530372321, 744340577

Offset

1,1

Comments

Primes of form x^8 + y^8 + z^8 where x, y, z > 0.

Links

Chai Wah Wu, Table of n, a(n) for n = 1..10000

Example

3 = 1^8 + 1^8 + 1^8;
6563 = 1^8 + 1^8 + 3^8;
72353 = 2^8 + 3^8 + 4^8, etc.

Mathematica

nn = 13; Select[Union[Plus @@@ (Tuples[Range[nn], {3}]^8)], # <= nn^8 && PrimeQ[#] &]

Prog

(PARI) list(lim)=my(v=List(), A, B, t); lim\=1; for(a=1, sqrtnint(lim-2, 8), A=a^8; for(b=1, min(sqrtnint(lim-A-1, 8), a), B=A+b^8; forstep(c=if(B%2, 2, 1), sqrtnint(lim-B, 8), 2, if(isprime(t=B+c^8), listput(v, t))))); Set(v) \\ Charles R Greathouse IV, Nov 05 2017

Crossrefs

Cf. A001016, A003381, A006686, A007490, A085317, A085318, A085319, A283017, A283018.

Sequence in context: A338412 A187879 A325052 * A056749 A281788 A134776

Adjacent sequences: A283016 A283017 A283018 * A283020 A283021 A283022

Keyword

nonn

Author

Ilya Gutkovskiy, Feb 26 2017

Status

approved