A046894 Numbers expressible as p^3 + q^3 with p, q prime in at least two ways.

6058655748, 6507811154, 12906787894, 20593712932, 140253191624, 293833825922, 1087909914364, 1103283061146, 1361780473538, 1421173058634, 1479220098876, 1633040181864, 2671279610454, 4162315049802, 5031989043172

Offset: 1

Author

David W. Wilson

Keywords

• nonn

Comments

All terms less than 2^63 are expressible in only two ways. Every term produces two terms in A125063.

Verified the above comment up to 2^64. - Toshitaka Suzuki, Jan 04 2017

Examples

			First few examples are
    6058655748 =   61^3 + 1823^3 = 1049^3 + 1699^3,
    6507811154 =   31^3 + 1867^3 =  397^3 + 1861^3,
   12906787894 =  593^3 + 2333^3 = 1787^3 + 1931^3,
   20593712932 =   71^3 + 2741^3 =  977^3 + 2699^3,
  140253191624 = 1321^3 + 5167^3 = 3853^3 + 4363^3,
  293833825922 = 1567^3 + 6619^3 = 3769^3 + 6217^3.
		

Links

• Toshitaka Suzuki, Table of n, a(n) for n = 1..2013 (terms < 2^64; first 1604 terms from T. D. Noe)
• C. Rivera, The prime version of the taxicab problem.

Crossrefs

Cf. A125063.

Programs

Mathematica

Sort[First /@ Select[Tally[Flatten[Table[p^3 + q^3, {p, Prime[Range[2000]]}, {q, Prime[Range[PrimePi[p - 1]]]}]]], Last[#] > 1 &]] (* Jayanta Basu, Jun 30 2013 *)