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A283017
Primes which are the sum of three nonzero 6th powers.
3
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
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
KEYWORD
nonn
AUTHOR
Ilya Gutkovskiy, Feb 26 2017
STATUS
approved