A083500 - OEIS

%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