A086121 -id:A086121 - cp's OEIS frontend

A086119 Numbers of the form p^3 + q^3, p, q primes.

16, 35, 54, 133, 152, 250, 351, 370, 468, 686, 1339, 1358, 1456, 1674, 2205, 2224, 2322, 2540, 2662, 3528, 4394, 4921, 4940, 5038, 5256, 6244, 6867, 6886, 6984, 7110, 7202, 8190, 9056, 9826, 11772, 12175, 12194, 12292, 12510, 13498, 13718, 14364

Offset: 1

Hollie L. Buchanan II, Jul 11 2003

nonn

			133 belongs to the sequence because it can be written as 2^3 + 5^3.

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

Cf. A001235, A003325, A045636, A045699, A086120, A086121.

sumList[x_List, y_List] := Module[{t = {}}, Do[t = Union[t, x[[i]] + y], {i, Length[x]}];  t]; nn = 10; Select[sumList[Prime[Range[nn]]^3, Prime[Range[nn]]^3], # < Prime[nn]^3 &]

More terms from Alexander Adamchuk, Nov 10 2006

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

Original entry on oeis.org

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

Hollie L. Buchanan II, Jul 11 2003

nonn

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.

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

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

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

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 *)

Corrected by T. D. Noe, Oct 04 2010

cp's OEIS Frontend

A086119 Numbers of the form p^3 + q^3, p, q primes.

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