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Numbers n > 1 such that 2^m == 1 (mod n^2), where m = A002326((n-1)/2).
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%I #40 Dec 11 2015 11:58:38

%S 1093,3511,7651,10533,14209,17555,22953,31599,42627,45643,52665,99463,

%T 136929,157995,228215,298389,410787,684645,2053935,3837523,11512569,

%U 19187615,26862661,34537707,49887799,57562845,80587983,134313305,149663397,172688535,241763949,249438995,349214593,402939915,448990191,748316985,1047643779,1208819745,1746072965,2244950955,3142931337,5238218895,15714656685

%N Numbers n > 1 such that 2^m == 1 (mod n^2), where m = A002326((n-1)/2).

%C A subsequence of A077816.

%C Odd numbers n > 1 such that A237292((n-1)/2) = 1.

%C Indices k such that A077816(k) is not in this sequence are 2, 13, 14, 16, 22, 24, 25, 27, 28, 30, ... - _Altug Alkan_, Dec 11 2015

%C There are no other terms, unless there are other Wieferich primes (A001220) besides 1093 and 3511. - _Max Alekseyev_, Dec 11 2015

%t Select[Range[10^6], Mod[2^MultiplicativeOrder[2, 2 ((# - 1)/2) + 1], #^2] == 1 &] (* _Michael De Vlieger_, Dec 11 2015 *)

%o (PARI) a002326(n) = znorder(Mod(2, 2*n+1));

%o a237292(n) = a002326(2*n*(n+1))/a002326(n);

%o for(n=1, 1e8, if(a237292(n)==1, print1(2*n+1, ", "))) \\ _Altug Alkan_, Dec 11 2015

%Y Cf. A002326, A077816, A237292.

%K nonn

%O 1,1

%A _Thomas Ordowski_, Dec 11 2015

%E More terms from _Altug Alkan_, Dec 11 2015

%E Missing terms a(28)-a(30) and further terms a(34)-a(43) added by _Max Alekseyev_, Dec 11 2015