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

1,1

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

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.

Formula

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

Example

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).

Mathematica

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

Prog

(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

Crossrefs

Subsequence of A024670.

Sequence in context: A220481 A144492 A192926 * A339998 A039522 A044367

Adjacent sequences: A120395 A120396 A120397 * A120399 A120400 A120401

Keyword

nonn,easy

Author

Tanya Khovanova, Jul 24 2007

Status

approved