login

Reminder: The OEIS is hiring a new managing editor, and the application deadline is January 26.

Numbers which are the sum of three cubes of distinct primes.
6

%I #22 May 09 2021 11:20:08

%S 160,378,476,495,1366,1464,1483,1682,1701,1799,2232,2330,2349,2548,

%T 2567,2665,3536,3555,3653,3871,4948,5046,5065,5264,5283,5381,6252,

%U 6271,6369,6587,6894,6992,7011,7118,7137,7210,7229,7235,7327,7453,8198,8217,8315

%N Numbers which are the sum of three cubes of distinct primes.

%C 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.

%H Chai Wah Wu, <a href="/A138854/b138854.txt">Table of n, a(n) for n = 1..10000</a> (terms 1..621 from R. J. Mathar)

%H <a href="/index/Su#ssq">Index to sequences related to sums of cubes</a>.

%F 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}

%p isA030078 := proc(n)

%p local f ;

%p if n < 8 then

%p false;

%p else

%p f := ifactors(n)[2] ;

%p if nops(f) = 1 and op(2,op(1,f)) = 3 then

%p true;

%p else

%p false;

%p end if;

%p end if;

%p end proc:

%p isA138854 := proc(n)

%p local i,j,p,q,r,rcub ;

%p for i from 1 do

%p p := ithprime(i) ;

%p if p^3+(p+1)^3+(p+2)^3 > n then

%p return false;

%p end if;

%p for j from i+1 do

%p q := ithprime(j) ;

%p rcub := n-q^3-p^3 ;

%p if rcub <= q^3 then

%p break;

%p fi ;

%p if isA030078(rcub) then

%p return true;

%p end if;

%p end do:

%p end do:

%p end proc:

%p for n from 5 do

%p if isA138854(n) then

%p print(n);

%p end if;

%p end do: # _R. J. Mathar_, Jun 09 2014

%t 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 *)

%o (PARI) isA138854(n)={ if( n%2, isA138853(n), isA120398(n-8)) }

%o for( n=1,10^4, isA138854(n) & print1(n", "))

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

%K nonn

%O 1,1

%A _M. F. Hasler_, Apr 13 2008