A258865 Numbers that are a sum of the cubes of three primes.

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

Offset

1,1

Comments

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.

Links

Reinhard Zumkeller, Table of n, a(n) for n = 1..10000

Formula

a(n) = A030078(i)+A030078(j)+A030078(k) for some triple (i,j,k).

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

Example

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.

Maple

A258865 := proc(lim)
    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:
A258865(30000) ;

Mathematica

lim = 15; Take[Sort@ DeleteDuplicates[Total /@ (Tuples[Prime@ Range@ lim, 3]^3)], 3 lim] (* Michael De Vlieger, Jun 12 2015 *)

Prog

(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
-- Reinhard Zumkeller, Jun 13 2015
(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

Crossrefs

Cf. A138854, A114923.

Cf. A030078, A258262 (subsequence).

Sequence in context: A087093 A118299 A302360 * A072096 A055480 A322843

Adjacent sequences: A258862 A258863 A258864 * A258866 A258867 A258868

Keyword

nonn

Author

R. J. Mathar, Jun 12 2015

Status

approved