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Integers n such that n^2 is the difference of two Lucas numbers (A000204).
2

%I #3 Feb 13 2013 02:04:27

%S 0,1,2,5,6,14,57

%N Integers n such that n^2 is the difference of two Lucas numbers (A000204).

%C This sequence is similar to the one for Fibonacci numbers (A219114) and appears to be finite also. See A221471 for an infinite version of this sequence.

%e The only known square differences of Lucas numbers:

%e 1^2 = L(3)-L(2) = 4-3,

%e 2^2 = L(4)-L(2) 7-3 = L(5)-L(4) = 11-7,

%e 5^2 = L(7)-l(3) = 29-4,

%e 6^2 = L(8)-L(5) = 47-11,

%e 14^2 = L(11)-L(2) = 199-3,

%e 57^2 = L(17)-L(12) = 3571-322.

%t t = Union[Flatten[Abs[Table[LucasL[n] - LucasL[i], {n, 120}, {i, n}]]]]; t2 = Select[t, IntegerQ[Sqrt[#]] &]; Sqrt[t2]

%Y Cf. A000032 (Lucas numbers), A113191 (difference of two Lucas numbers).

%Y Cf. A219114 (corresponding sequence for Fibonacci numbers).

%K nonn

%O 1,3

%A _T. D. Noe_, Feb 13 2013