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%I #20 Feb 26 2014 00:45:29
%S 1,3,7,73,601,8191,262657,8640661
%N Numbers n=k^2-k+1 such that 2^k == 1 (mod n).
%C The elements of this sequence are elements of the sequence A002061 (Central polygonal numbers).
%C The first composite number is 8640661 = 31 * 211 * 1321 (31 and 211 are elements of the sequence A002061).
%C No more terms up to 3773299855577673.
%e k = 9;
%e n = k^2 - k + 1 = 81 - 9 + 1 = 73;
%e 2^9 == 1 (mod 73).
%o (PARI) for(k=1,10^9,n=k^2-k+1;if( lift(Mod(2,n)^k)==1,print1(n,", "))); /* _Joerg Arndt_, Jun 03 2011 */
%K nonn
%O 1,2
%A _Alzhekeyev Ascar M_, Jun 03 2011
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