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 2019-10-17, 01:17 #1 miket   May 2013 32 Posts Need more items for sequence 17, 257, 641, 65537, … Let n be an odd positive integer, Let o=ordn2 be the order of 2 modulo n and m the period of 1/n, k is number of distinct odd residues contained in set {2^1,2^2,...,2^{n−1}} modulo n. If odd part of o,m and k is 1 and k divide n-1, then n is item in the sequence 17, 257, 641, 65537, …. 167772161 also is item.It seems all known items in the sequence are Fermat factors and divide 2^(2^100) - 1 and 10^(10^100) - 1. Here's my PARI/GP code to check numbers(there's large space left for improve): Code: ` oddres(n)=if(n<2,0,n>>valuation(n,2)) ck(n) = { my(l=List(),m=if(1