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

%I #6 Feb 17 2018 20:02:06

%S 1,2,3,1,4,1,7,4,1,5,1,2,3,8,15,7,16,17,1,2,3,21,12,1,25,14,27,4,1,2,

%T 1,2,3,1,18,17,35,38,27,6,1,2,3,20,45,1,24,1,15,44,3,5,8,13,49,2,55,

%U 53,1,2,1,2,3,15,64,24,67,44,47,69,1,1,3,38,75,5,76,10,1,2,3,30

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

%H Clark Kimberling, <a href="/A214967/b214967.txt">Table of n, a(n) for n = 2..1000</a>

%e Write x#y if x|y is false; then 8#33, 7#32, 6#31, 5|30 so a(9) = 4.

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

%Y Cf. A214968.

%K nonn,easy

%O 2,2

%A _Clark Kimberling_, Jul 31 2012