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a(n) is the least m > 0 such that Lucas(n-m) divides Fibonacci(n+m).
2

%I #6 Feb 17 2018 20:01:49

%S 1,1,3,3,2,5,7,3,6,9,4,11,10,5,15,15,6,17,12,7,18,21,8,15,22,9,20,27,

%T 10,29,31,11,30,21,12,35,34,13,24,39,14,41,36,15,42,45,16,35,30,17,44,

%U 51,18,33,40,19,54,57,20,59,58,21,63,39,22,65,60,23,42,69,24

%N a(n) is the least m > 0 such that Lucas(n-m) divides Fibonacci(n+m).

%H Clark Kimberling, <a href="/A214919/b214919.txt">Table of n, a(n) for n = 2..1000</a>

%e Write x#y if x|y is false; then 47#55, 29#89, 18|144 so a(9) = 3.

%t Table[m = 1; While[! Divisible[Fibonacci[n+m],LucasL[n-m]], m++]; m, {n, 2, 100}]

%Y Cf. A214920.

%K nonn,easy

%O 2,3

%A _Clark Kimberling_, Jul 30 2012