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

Author

Ilya Gutkovskiy, Feb 26 2017

Keywords

• nonn

Comments

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

Examples

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

Links

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

Crossrefs

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

Programs

Mathematica

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

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