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A086120 Natural numbers of the form p^3 - q^3, where p and q are primes. 4
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 (list; graph; refs; listen; history; text; internal format)
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.

MAPLE

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]]

MATHEMATICA

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]]] [From 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

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Last modified September 22 19:04 EDT 2018. Contains 315270 sequences. (Running on oeis4.)