A111032 - OEIS

%I #6 Jan 05 2025 19:51:38

%S 29,169,194,433,985,1325,2897,5741,6466,7561,9077,14701,33461,37666,

%T 43261,51641,62210,96557,135137,195025,294685,426389,499393,646018,

%U 925765,1136689,1278818,1441889,1686049,2012674,2423525,2922509,3276509

%N Non-Fibonacci Markoff numbers.

%C Complement(A002559, A000045)

%H Anitha Srinivasan, <a href="https://web.archive.org/web/2024*/https://www.fq.math.ca/Papers1/58-5/srinivasan.pdf">The Markoff-Fibonacci Numbers</a>, Fibonacci Quart. 58 (2020), no. 5, 222-228.

%t m = {1}; Do[x = m[[i]]; y = m[[j]]; a = (3*x*y + Sqrt[ -4*x^2 - 4*y^2 + 9*x^2*y^2])/2; b = (3*x*y + Sqrt[ -4*x^2 - 4*y^2 + 9*x^2*y^2])/2; If[ IntegerQ[a], m = Union[ Join[m, {a}]]]; If[ IntegerQ[b], m = Union[ Join[m, {b}]]], {n, 8}, {i, Length[m]}, {j, i}]; Complement[ Take[m, 50], Fibonacci /@ Range[38]]

%Y Cf. A000045, A002559.

%K nonn

%O 1,1

%A _Robert G. Wilson v_, Oct 04 2005