This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A113191 #13 Jan 02 2025 12:51:09
%S A113191 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,
%T A113191 44,45,46,47,58,65,69,72,73,74,75,76,94,105,112,116,119,120,121,122,
%U A113191 123,152,170,181,188,192,195,196,197,198,199,246,275,293,304
%N A113191 Difference of two Lucas numbers.
%C A113191 Also the sum of consecutive Lucas numbers because the difference L(i) - L(j) equals the sum L(j+1) + ... + L(i+2).
%C A113191 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
%H A113191 T. D. Noe, <a href="/A113191/b113191.txt">Table of n, a(n) for n = 1..1000</a>
%t A113191 Lucas[n_] := Fibonacci[n+1]+Fibonacci[n-1]; Union[Flatten[Table[Lucas[n]-Lucas[i], {n, 13}, {i, 0, n-2}]]]
%Y A113191 Cf. A000032 (Lucas numbers), A007298 (difference of two Fibonacci numbers).
%Y A113191 Cf. A221471, A221472 (square root of squares in this sequence).
%K A113191 nonn
%O A113191 1,3
%A A113191 _T. D. Noe_, Oct 17 2005