A120398 - OEIS

%I #16 Mar 31 2022 13:23:47

%S 35,133,152,351,370,468,1339,1358,1456,1674,2205,2224,2322,2540,3528,

%T 4921,4940,5038,5256,6244,6867,6886,6984,7110,7202,8190,9056,11772,

%U 12175,12194,12292,12510,13498,14364,17080,19026,24397,24416,24514

%N Sums of two distinct prime cubes.

%C If an element of this sequence is odd, it must be of the form a(n)=8+p^3, else it is a(n)=p^3+q^3 with two primes p>q>2. - _M. F. Hasler_, Apr 13 2008

%H M. F. Hasler and Charles R Greathouse IV, <a href="/A120398/b120398.txt">Table of n, a(n) for n = 1..10000</a> (first 284 terms from Hasler)

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

%F A120398 = (A030078 + A030078) - 2*A030078 = 8+(A030078\{8}) U { A030078(m)+A030078(n) ; 1<m<n } - _M. F. Hasler_, Apr 13 2008

%e 2^3+3^3=35=a(1), 2^3+5^3=133=a(2), 3^3+5^3=152=a(3), 2^3+7^3=351=a(4).

%t Select[Sort[ Flatten[Table[Prime[n]^3 + Prime[k]^3, {n, 15}, {k, n - 1}]]], # <= Prime[15^3] &]

%o (PARI) isA030078(n)=n==round(sqrtn(n,3))^3 && isprime(round(sqrtn(n,3)))  \\ _M. F. Hasler_, Apr 13 2008

%o (PARI) isA120398(n)={ n%2 & return(isA030078(n-8)); n<35 & return; forprime( p=ceil( sqrtn( n\2+1,3)),sqrtn(n-26.5,3), isA030078(n-p^3) & return(1))} \\ _M. F. Hasler_, Apr 13 2008

%o (PARI) for( n=1,10^6, isA120398(n) & print1(n",")) \\ - _M. F. Hasler_, Apr 13 2008

%o (PARI) list(lim)=my(v=List()); lim\=1; forprime(q=3,sqrtnint(lim-8,3), my(q3=q^3); forprime(p=2,min(sqrtnint(lim-q3,3),q-1), listput(v,p^3+q3))); Set(v) \\ _Charles R Greathouse IV_, Mar 31 2022

%Y Subsequence of A024670.

%K nonn,easy

%O 1,1

%A _Tanya Khovanova_, Jul 24 2007