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a(n) is the period of the Leonardo numbers (A001595) modulo n.
3

%I #12 Sep 13 2024 08:11:36

%S 1,1,8,3,20,8,16,6,24,20,10,24,28,16,40,12,36,24,18,60,16,10,48,24,

%T 100,28,72,48,14,40,30,24,40,36,80,24,76,18,56,60,40,16,88,30,120,48,

%U 32,24,112,100,72,84,108,72,20,48,72,14,58,120,60,30,48,48,140

%N a(n) is the period of the Leonardo numbers (A001595) modulo n.

%C See A376081 for more information.

%H Paolo Xausa, <a href="/A376082/b376082.txt">Table of n, a(n) for n = 1..10000</a>

%F Apparently, a(2*k) = A001175(k), for k >= 1.

%t A376082[n_] := If[n < 3, 1, Module[{k = 1}, NestWhile[Mod[2*Fibonacci[++k] - 1, n] &, 1, {#, #2} != {1, n-1} &, {3, 2}]; k]];

%t Array[A376082, 100]

%Y Row lengths of A376081.

%Y Cf. A001175.

%K nonn

%O 1,3

%A _Paolo Xausa_, Sep 10 2024