A086120 Natural numbers of the form p^3 - q^3, where p and q are primes.

19, 98, 117, 218, 316, 335, 866, 988, 1206, 1304, 1323, 1854, 1946, 2072, 2170, 2189, 2716, 3582, 4570, 4662, 4788, 4886, 4905, 5308, 5402, 5528, 6516, 6734, 6832, 6851, 7254, 9970, 10586, 10836, 11824, 12042, 12140, 12159, 12222, 17530, 17624, 18268

Offset: 1

Author

Hollie L. Buchanan II, Jul 11 2003

Keywords

• nonn

Comments

To find all differences p^3 - q^3 less than N, it is required that all primes p and q up to sqrt(N/6) be tested.

Examples

			117 belongs to the sequence because it can be written as 5^3 - 2^3.
		

Links

• T. D. Noe, Table of n, a(n) for n=1..10000

Crossrefs

Cf. A086119, A086121. Also see A045636, A045699.

Programs

Mathematica

sumList[x_List, y_List] := (punchline = {}; Do[punchline = Union[punchline, x[[i]] + y], {i, Length[x]}]; punchline); posPart[x_List] := (punchline = {}; Do[If[x[[i]] > 0, punchline = Union[punchline, {x[[i]]}]], {i, Length[x]}]; punchline); posPart[sumList[Prime[Range[10]]^3, - Prime[Range[10]]^3]]
nn=10^5; Union[Reap[Do[n=Prime[i]^3-Prime[j]^3; If[n<=nn, Sow[n]], {i,PrimePi[Sqrt[nn/6]]}, {j,i-1}]][[2,1]]] (* T. D. Noe, Oct 04 2010 *)
With[{upto=20000},Select[Abs[#[[1]]-#[[2]]]&/@Subsets[Prime[ Range[ Sqrt[ upto/6]]]^3,{2}]//Union,#<=upto&]] (* Harvey P. Dale, Dec 10 2017 *)

Extensions

Corrected by T. D. Noe, Oct 04 2010