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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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified July 30 07:41 EDT 2021. Contains 346348 sequences. (Running on oeis4.)