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%I #16 Mar 15 2023 11:12:29
%S 16,19,35,54,98,117,133,152,218,250,316,335,351,370,468,686,866,988,
%T 1206,1304,1323,1339,1358,1456,1674,1854,1946,2072,2170,2189,2205,
%U 2224,2322,2540,2662,2716,3528,3582,4394,4570,4662,4788,4886,4905,4921,4940,5038
%N Positive sums or differences of two cubes of primes.
%H Hans Havermann and T. D. Noe, <a href="/A086121/b086121.txt">Table of n, a(n) for n = 1..20000</a>.
%e 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.
%t 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 *)
%t 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 *)
%Y Cf. A086119, A086120. Also see A045636, A045699.
%K nonn
%O 1,1
%A _Hollie L. Buchanan II_, Jul 11 2003
%E 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.
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