A086121 Positive sums or differences of two cubes of primes.

16, 19, 35, 54, 98, 117, 133, 152, 218, 250, 316, 335, 351, 370, 468, 686, 866, 988, 1206, 1304, 1323, 1339, 1358, 1456, 1674, 1854, 1946, 2072, 2170, 2189, 2205, 2224, 2322, 2540, 2662, 2716, 3528, 3582, 4394, 4570, 4662, 4788, 4886, 4905, 4921, 4940, 5038

Offset: 1

Author

Hollie L. Buchanan II, Jul 11 2003

Keywords

• nonn

Examples

			117 and 133 each belong to the (set) sequence because can be written as 117 = 5^3 - 2^3 and 133 = 5^3 + 2^3.
		

Links

• Hans Havermann and T. D. Noe, Table of n, a(n) for n = 1..20000.

Crossrefs

Cf. A086119, A086120. Also see A045636, A045699.

Programs

Mathematica

nn=10^6; td=Reap[Do[n=Prime[i]^3-Prime[j]^3; If[n<=nn, Sow[n]], {i,PrimePi[Sqrt[nn/6]]}, {j,i-1}]][[2,1]]; ts=Reap[Do[n=Prime[i]^3+Prime[j]^3; If[n<=nn, Sow[n]], {i,PrimePi[nn^(1/3)]}, {j,i}]][[2,1]]; Union[td,ts] (* T. D. Noe, Oct 04 2010 *)
n = 100; Select[Sort@Flatten@ Table[Prime[i]^3 + (-1)^k Prime[j]^3, {i, n}, {j, i}, {k, 2}], 0 < # < (Prime[n] + 2)^3 - Prime[n]^3 &] (* Ray Chandler, Oct 05 2010 *)

Extensions

Edited by N. J. A. Sloane, Oct 05 2010 to remove a discrepancy between the terms of the sequence and the b-file. The old Mma program and b-file were wrong.