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

Author

R. J. Mathar, Jun 12 2015

Keywords

• nonn

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.

Examples

			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.
		

Links

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

Crossrefs

Cf. A138854, A114923.

Cf. A030078, A258262 (subsequence).

Programs

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

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 *)

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

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