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a(n) = n^(2*n-1) mod (2*n-1).
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%I #48 Aug 24 2022 10:10:06

%S 0,2,3,4,8,6,7,2,9,10,8,12,18,26,15,16,29,2,19,5,21,22,8,24,18,32,27,

%T 32,50,30,31,8,63,34,26,36,37,32,30,40,80,42,8,11,45,32,35,22,49,35,

%U 51,52,8,54,55,14,57,87,8,2,94,77,68,64,113,66,53,107,69

%N a(n) = n^(2*n-1) mod (2*n-1).

%C If a(n) = n then 2*n-1 is prime or Fermat pseudoprime to base 2.

%t a[n_] := PowerMod[n, 2*n - 1, 2*n - 1]; Array[a, 100] (* _Amiram Eldar_, Jul 23 2022 *)

%o (PARI) a(n)=n^(2*n-1)%(2*n-1)

%o (PARI) a(n)=lift(Mod(n, 2*n-1)^(2*n-1)) \\ _Rémy Sigrist_, Jul 21 2022

%o (Python)

%o def a(n): return pow(n, 2*n-1, 2*n-1)

%o print([a(n) for n in range(1, 70)]) # _Michael S. Branicky_, Jul 23 2022

%Y Cf. A000040, A001567, A006254, A085524, A174166, A179976.

%K nonn

%O 1,2

%A _Jonas Kaiser_, Jul 20 2022