A120398 Sums of two distinct prime cubes.

35, 133, 152, 351, 370, 468, 1339, 1358, 1456, 1674, 2205, 2224, 2322, 2540, 3528, 4921, 4940, 5038, 5256, 6244, 6867, 6886, 6984, 7110, 7202, 8190, 9056, 11772, 12175, 12194, 12292, 12510, 13498, 14364, 17080, 19026, 24397, 24416, 24514

Offset: 1

Author

Tanya Khovanova, Jul 24 2007

Keywords

• nonn
• easy

Comments

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

Examples

			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).
		

Links

• M. F. Hasler and Charles R Greathouse IV, Table of n, a(n) for n = 1..10000 (first 284 terms from Hasler)
• Index to sequences related to sums of cubes.

Crossrefs

Subsequence of A024670.

Programs

Mathematica

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

PARI

isA030078(n)=n==round(sqrtn(n,3))^3 && isprime(round(sqrtn(n,3)))  \\ M. F. Hasler, Apr 13 2008

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

PARI

for( n=1,10^6, isA120398(n) & print1(n",")) \\ - M. F. Hasler, Apr 13 2008

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

Formula

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