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A258865
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Numbers that are a sum of the cubes of three primes.
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4
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24, 43, 62, 81, 141, 160, 179, 258, 277, 359, 375, 378, 397, 476, 495, 593, 694, 713, 811, 1029, 1347, 1366, 1385, 1464, 1483, 1581, 1682, 1701, 1799, 2017, 2213, 2232, 2251, 2330, 2349, 2447, 2548, 2567, 2665, 2670, 2689, 2787, 2883, 3005, 3536, 3555
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OFFSET
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1,1
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COMMENTS
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The subsequence of cubes in the sequence starts 505^3, 535^3, 709^3, 865^3, 1033^3, 1037^3, 1067^3, 1133^3, 1513^3, ... See A258262.
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LINKS
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FORMULA
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By a counting argument a(n) >> n log^3 n and hence the sequence is of density 0. - Charles R Greathouse IV, Aug 09 2021
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EXAMPLE
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2^3+2^3+2^3=24. 2^3+2^3+3^3=43. 2^3+3^3+3^3=62. 3^3+3^3+3^3=81.
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MAPLE
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local a, p, q, r ;
a := {} ;
p := 2 ;
while p^3 < lim do
q := p ;
while p^3 +q^3< lim do
r := q ;
while p^3+q^3+r^3 <= lim do
a := a union {p^3+q^3+r^3} ;
r := nextprime(r) ;
end do:
q := nextprime(q) ;
end do:
p := nextprime(p) ;
end do ;
a ;
end proc:
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MATHEMATICA
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lim = 15; Take[Sort@ DeleteDuplicates[Total /@ (Tuples[Prime@ Range@ lim, 3]^3)], 3 lim] (* Michael De Vlieger, Jun 12 2015 *)
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PROG
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(Haskell)
import Data.Set (singleton, deleteFindMin, fromList)
import qualified Data.Set as Set (union)
import qualified Data.List.Ordered as List (union)
a258865 n = a258865_list !! (n-1)
a258865_list = tail $ f (singleton 1) 1 [] [] a030078_list where
f s z vs qcs pcs'@(pc:pcs)
| m < z = m : f s' z vs qcs pcs'
| otherwise = f (Set.union s $ fromList $ map (+ pc) ws)
pc ws (pc:qcs) pcs
where ws = List.union vs $ map (+ pc) (pc : qcs)
(m, s') = deleteFindMin s
(PARI) list(lim)=my(v=List(), P=apply(p->p^3, primes(sqrtnint(lim\=1, 3)))); foreach(P, p, foreach(P, q, my(s=p+q, t); for(i=1, #P, t=s+P[i]; if(t>lim, break); listput(v, t)))); Set(v) \\ Charles R Greathouse IV, Aug 09 2021
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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