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A221472
Integers n such that n^2 is the difference of two Lucas numbers (A000204).
2
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.
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
KEYWORD
nonn
AUTHOR
T. D. Noe, Feb 13 2013
STATUS
approved