A138854 Numbers which are the sum of three cubes of distinct primes.

160, 378, 476, 495, 1366, 1464, 1483, 1682, 1701, 1799, 2232, 2330, 2349, 2548, 2567, 2665, 3536, 3555, 3653, 3871, 4948, 5046, 5065, 5264, 5283, 5381, 6252, 6271, 6369, 6587, 6894, 6992, 7011, 7118, 7137, 7210, 7229, 7235, 7327, 7453, 8198, 8217, 8315

Offset: 1

Author

M. F. Hasler, Apr 13 2008

Keywords

• nonn

Comments

This is a subsequence of A024975. The odd terms of this sequence are A138853, the even terms are 8+{ even terms of A120398 }. Thus primes in this sequence, A137365, are the same as primes in A138853.

Links

• Chai Wah Wu, Table of n, a(n) for n = 1..10000 (terms 1..621 from R. J. Mathar)
• Index to sequences related to sums of cubes.

Crossrefs

Cf. A024975 (a^3+b^3+c^3, a>b>c>0), A138853 (odd terms of this), A120398, A137365 (primes in A138853 / A138854).

Programs

Maple

isA030078 := proc(n)
    local f ;
    if n < 8 then
        false;
    else
        f := ifactors(n)[2] ;
        if nops(f) = 1 and op(2,op(1,f)) = 3 then
            true;
        else
            false;
        end if;
    end if;
end proc:
isA138854 := proc(n)
    local i,j,p,q,r,rcub ;
    for i from 1 do
        p := ithprime(i) ;
        if p^3+(p+1)^3+(p+2)^3 > n then
            return false;
        end if;
        for j from i+1 do
            q := ithprime(j) ;
            rcub := n-q^3-p^3 ;
            if rcub <= q^3 then
                break;
            fi ;
            if isA030078(rcub) then
                return true;
            end if;
        end do:
    end do:
end proc:
for n from 5 do
    if isA138854(n) then
        print(n);
    end if;
end do: # R. J. Mathar, Jun 09 2014

Mathematica

f[upto_]:=Module[{maxp=PrimePi[Floor[Power[upto, (3)^-1]]]}, Select[Union[Total/@(Subsets[Prime[Range[maxp]],{3}]^3)],#<=upto&]]; f[9000]  (* Harvey P. Dale, Mar 21 2011 *)

PARI

isA138854(n)={ if( n%2, isA138853(n), isA120398(n-8)) }
for( n=1,10^4, isA138854(n) & print1(n", "))

Formula

A138854 = { p(i)^3+p(j)^3+p(k)^3 ; i>j>k>0 } = A138853 union { p(i)^3+p(j)^3+8 ; i>j>1}