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%I #40 Jun 27 2024 09:01:24
%S 1,1105,1387,1729,2047,2701,2821,3277,4033,4369,4681,5461,6601,7957,
%T 8911,10261,10585,11305,13741,13747,13981,14491,15709,15841,16705,
%U 18721,19951,23377,29341,30121,30889,31417,31609,31621,34945,39865,41041,41665,42799,46657,49141,49981
%N Nonprimes k such that 9*k divides 2^(k-1) - 1.
%C Original name was: Nonprimes n of the form 6m+1 such that (2^(n-1) mod n)=(4^(n-1) mod n)=(8^(n-1) mod n)=..=(k^(n-1) mod n) for k=2,4,8,..,smallest power of 2>n.
%H Vincenzo Librandi and T. D. Noe, <a href="/A175521/b175521.txt">Table of n, a(n) for n = 1..1000</a>
%e 1 is a term because it is a nonprime and 9*1 = 9 divides 2^(1-1) - 1 = 0.
%t n = 1; t = {}; While[Length[t] < 100, While[PrimeQ[n] || PowerMod[2, n-1, 9*n] != 1, n = n + 2]; AppendTo[t, n]; n = n + 2]; t (* _T. D. Noe_, Jul 25 2011 *)
%o (PARI) p=0;forprime(q=2,1e5,for(n=p+1,q-1,if(Mod(2,9*n)^(n-1)==1,print1(n", ")));p=q) \\ _Charles R Greathouse IV_, Jul 24 2011
%Y Subsequence of A001567.
%Y Cf. A000079, A091300.
%K nonn
%O 1,2
%A _Juri-Stepan Gerasimov_, Dec 18 2010
%E Name changed by _Arkadiusz Wesolowski_, Jul 23 2011