A221472 Integers n such that n^2 is the difference of two Lucas numbers (A000204).

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

Offset: 1

Author

T. D. Noe, Feb 13 2013

Keywords

• nonn

Comments

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.

Examples

			The only known square differences of Lucas numbers:
1^2 = L(3)-L(2) = 4-3,
2^2 = L(4)-L(2) 7-3 = L(5)-L(4) = 11-7,
5^2 = L(7)-l(3) = 29-4,
6^2 = L(8)-L(5) = 47-11,
14^2 = L(11)-L(2) = 199-3,
57^2 = L(17)-L(12) = 3571-322.
		

Crossrefs

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

Cf. A219114 (corresponding sequence for Fibonacci numbers).

Programs

Mathematica

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