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

1,1

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.

Links

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

Example

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

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 *)

Crossrefs

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

Sequence in context: A142170 A069593 A299733 * A129701 A221746 A241236

Adjacent sequences: A086117 A086118 A086119 * A086121 A086122 A086123

Keyword

nonn

Author

Hollie L. Buchanan II, Jul 11 2003

Extensions

Corrected by T. D. Noe, Oct 04 2010

Status

approved