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%I #7 Aug 23 2014 13:26:27
%S 6,11,18,27,38,51,2,83,29,123,146,171,43,38,258,291,326,1,51,443,174,
%T 531,578,627,678,2,10,530,902,963,473,1091,1158,1227,3,25,438,1523,66,
%U 1683,1766,330,1042,2027,46,2211,2306,2403,70,2603,2706,417,2918,73
%N Smallest k such that n*(n+k) + 1 is a cube.
%C For all n, n*(n+k) + 1 is a square for k = 2.
%C Differs from A102305 at positions listed by A102306.
%e a(7) = 2 as 7*9 + 1 = 64 = 4^3, though 66 also qualifies but 2<66.
%t Do[k = 0; While[i = n(n + k) + 1; !IntegerQ[i^(1/3)], k++ ]; Print[k], {n, 1, 55}]
%Y Cf. A083501.
%K nonn
%O 1,1
%A _Amarnath Murthy_ and Meenakshi Srikanth (menakan_s(AT)yahoo.com), May 03 2003
%E Edited and extended by _Robert G. Wilson v_, May 11 2003
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