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%I #35 Nov 01 2023 09:57:53
%S 6058655748,6507811154,12906787894,20593712932,140253191624,
%T 293833825922,1087909914364,1103283061146,1361780473538,1421173058634,
%U 1479220098876,1633040181864,2671279610454,4162315049802,5031989043172
%N Numbers expressible as p^3 + q^3 with p, q prime in at least two ways.
%C All terms less than 2^63 are expressible in only two ways. Every term produces two terms in A125063.
%C Verified the above comment up to 2^64. - _Toshitaka Suzuki_, Jan 04 2017
%H Toshitaka Suzuki, <a href="/A046894/b046894.txt">Table of n, a(n) for n = 1..2013</a> (terms < 2^64; first 1604 terms from T. D. Noe)
%H C. Rivera, <a href="http://www.primepuzzles.net/puzzles/puzz_090.htm">The prime version of the taxicab problem</a>.
%e First few examples are
%e 6058655748 = 61^3 + 1823^3 = 1049^3 + 1699^3,
%e 6507811154 = 31^3 + 1867^3 = 397^3 + 1861^3,
%e 12906787894 = 593^3 + 2333^3 = 1787^3 + 1931^3,
%e 20593712932 = 71^3 + 2741^3 = 977^3 + 2699^3,
%e 140253191624 = 1321^3 + 5167^3 = 3853^3 + 4363^3,
%e 293833825922 = 1567^3 + 6619^3 = 3769^3 + 6217^3.
%t Sort[First /@ Select[Tally[Flatten[Table[p^3 + q^3, {p, Prime[Range[2000]]}, {q, Prime[Range[PrimePi[p - 1]]]}]]], Last[#] > 1 &]] (* _Jayanta Basu_, Jun 30 2013 *)
%Y Cf. A125063.
%K nonn
%O 1,1
%A _David W. Wilson_
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