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

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

Offset

1,3

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.

Links

Table of n, a(n) for n=1..7.

Example

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.

Mathematica

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

Crossrefs

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

Cf. A219114 (corresponding sequence for Fibonacci numbers).

Sequence in context: A057302 A237352 A109784 * A076624 A205385 A341373

Adjacent sequences: A221469 A221470 A221471 * A221473 A221474 A221475

Keyword

nonn

Author

T. D. Noe, Feb 13 2013

Status

approved