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%I #11 Feb 14 2018 08:09:17
%S 1,1,1,3,4,3,4,1,3,6,4,5,6,5,11,8,8,3,5,4,8,16,4,7,10,5,22,3,13,23,10,
%T 4,4,20,5,12,12,8,3,9,22,9,3,11,25,4,8,6,14,14,9,38,4,31,32,5,14,18,4,
%U 3,19,8,56,16,16,28,25,22,31,50,7,19,11,10,43,46,5
%N a(n) is the smallest k such that k^8 = 16 (mod 2*n-1).
%C Motivated by Crandall & Pomerance, Exercise 2.1 p. 108: "Prove that 16 is, modulo any odd number, an eighth power".
%D R. Crandall and C. Pomerance, Prime Numbers: A Computational Perspective, Springer, NY, 2001; see Exercise 2.1 p. 108.
%e a(9)=3 since for odd number 2*9-1=17, 3^8 = 16 (mod 17).
%t Table[SelectFirst[Range@ 1000, Mod[#^8, 2 n - 1] == Mod[16, 2 n - 1] &], {n, 77}] (* _Michael De Vlieger_, Mar 24 2016, Version 10 *)
%o (PARI) a(n) = { my(m = 2*n-1, k = 1); while(Mod(k, m)^8 != 16, k++); k;}
%K nonn
%O 1,4
%A _Michel Marcus_, Mar 23 2016
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