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a(n) is the smallest distance between a pair of equal terms in the sequence s(0) = 1, s(1) = r, and s(k) = s(k-1)^2/(4*s(k-2)) mod p for k>=2, where p = prime(n) (=A000040(n)) and r is a primitive root modulo p.
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%I #6 Sep 11 2024 23:01:22

%S 2,2,2,2,2,16,2,2,2,6,2,8,6,2,2,2,2,2,2,8,2,2,8,32,2,2,2,54,16,18,2,8,

%T 2,2,50,6,2,2,2,2,2,2,64,2,2,2,6,2,6,8,2,80,250,256,2,2,2,6,8,6,2,18,

%U 2,8,2,22,16,2,2,32,2,2,2,2,2,2,18,16,8,2,2,10,432,6,2,64,24,2,2,2,2,2,2,6,2,2,8,2,2,2,2,2,8,10,64,2,16,2,24,2,2,8,2,14,640,6

%N a(n) is the smallest distance between a pair of equal terms in the sequence s(0) = 1, s(1) = r, and s(k) = s(k-1)^2/(4*s(k-2)) mod p for k>=2, where p = prime(n) (=A000040(n)) and r is a primitive root modulo p.

%C a(n) does not depend on the choice of a primitive root r modulo prime(n).

%C a(n) = prime(n) - 1 iff prime(n) is in A376008.

%C a(n) = 2 iff prime(n) is in A216371.

%C a(n) > 2 iff prime(n) is in A268923.

%Y Cf. A216371, A268923, A376008.

%K nonn

%O 2,1

%A _Max Alekseyev_, Sep 05 2024