A113191 - OEIS

A113191

Difference of two Lucas numbers.

0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 14, 15, 16, 17, 18, 22, 25, 26, 27, 28, 29, 36, 40, 43, 44, 45, 46, 47, 58, 65, 69, 72, 73, 74, 75, 76, 94, 105, 112, 116, 119, 120, 121, 122, 123, 152, 170, 181, 188, 192, 195, 196, 197, 198, 199, 246, 275, 293, 304

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OFFSET

1,3

COMMENTS

Also the sum of consecutive Lucas numbers because the difference L(i) - L(j) equals the sum L(j+1) + ... + L(i+2).

Conjecture: L(m) - L(n) with m > 1 and m > n >= 0 is a perfect power but not a square only for (m,n) = (7,0), (5,2). This has been verified for n < m <= 500. Note that L(7) - L(0) = 29 - 2 = 3^3 and L(5) - L(2) = 11 - 3 = 2^3. - Zhi-Wei Sun, Jan 02 2025

LINKS

T. D. Noe, Table of n, a(n) for n = 1..1000

MATHEMATICA

Lucas[n_] := Fibonacci[n+1]+Fibonacci[n-1]; Union[Flatten[Table[Lucas[n]-Lucas[i], {n, 13}, {i, 0, n-2}]]]

CROSSREFS

Cf. A000032 (Lucas numbers), A007298 (difference of two Fibonacci numbers).

Cf. A221471, A221472 (square root of squares in this sequence).

Sequence in context: A130574 A023780 A035064 * A191923 A191922 A230776

Adjacent sequences: A113188 A113189 A113190 * A113192 A113193 A113194

KEYWORD

nonn

AUTHOR

T. D. Noe, Oct 17 2005

STATUS

approved