A283017 Primes which are the sum of three nonzero 6th powers.

3, 857, 1459, 4889, 50753, 51481, 66377, 119107, 210961, 262937, 308801, 525017, 531569, 539633, 562691, 766739, 797681, 840241, 1000793, 1046657, 1078507, 1772291, 1864873, 2303003, 2834443, 2986777, 3032641, 3107729, 3365777, 4757609, 4804201, 5135609, 5987593, 7530329, 7534361, 7743529, 8061041

Offset

1,1

Comments

Primes of form x^6 + y^6 + z^6 where x, y, z > 0.

Links

Robert Israel, Table of n, a(n) for n = 1..10000

Example

3 = 1^6 + 1^6 + 1^6;
857 = 2^6 + 2^6 + 3^6;
1459 = 1^6 + 3^6 + 3^6, etc.

Maple

N:= 10^8: # to get all terms <= N
S:= [seq(i^6, i=1..floor(N^(1/6)))]:
S3:= {seq(seq(seq(S[i]+S[j]+S[k], k=1..j), j=1..i), i=1..nops(S))}:
sort(convert(select(t -> t <= N and isprime(t), S3), list)); # Robert Israel, Mar 09 2017

Mathematica

nn = 15; Select[Union[Plus @@@ (Tuples[Range[nn], {3}]^6)], # <= nn^6 && PrimeQ[#] &]

Prog

(PARI) list(lim)=my(v=List(), a6, a6b6, t); lim\=1; for(a=1, sqrtnint(lim-2, 6), a6=a^6; for(b=1, min(sqrtnint(lim-a6-1, 6), a), a6b6=a6+b^6; forstep(c=if(a6b6%2, 2, 1), min(sqrtnint(lim-a6b6, 6), b), 2, if(isprime(t=a6b6+c^6), listput(v, t))))); Set(v) \\ Charles R Greathouse IV, Mar 09 2017

Crossrefs

Cf. A001014, A003359, A007490, A085317, A085318, A085319, A283018, A283019.

Sequence in context: A020525 A252762 A341574 * A093189 A163430 A203688

Adjacent sequences: A283014 A283015 A283016 * A283018 A283019 A283020

Keyword

nonn

Author

Ilya Gutkovskiy, Feb 26 2017

Status

approved