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A273618 Numbers m = 2*k+1 where k is odd with the property that 3^k mod m = 1 and k^k mod m = 1.

%I A273618 #22 Aug 23 2023 08:37:23
%S A273618 11,59,83,107,131,179,227,251,347,419,443,467,491,563,587,659,683,827,
%T A273618 947,971,1019,1091,1163,1187,1259,1283,1307,1427,1451,1499,1523,1571,
%U A273618 1619,1667,1787,1811,1907,1931,1979,2003,2027,2099,2243,2267
%N A273618 Numbers m = 2*k+1 where k is odd with the property that 3^k mod m = 1 and k^k mod m = 1.
%C A273618 All composites in this sequence are 2-pseudoprimes, see A001567, and strong pseudoprimes to base 2, A001262.
%C A273618 The subsequence of these composites begins: 143193768587, 440097066011, 1188059560451, 1392770336147, 1640446291859, 2526966350771, 3639120872171, 3989703695867, 4202422108523, ....
%C A273618 Perhaps this sequence contains all the terms of the sequence A107007 (except 3) or A168539.
%H A273618 Robert Israel, <a href="/A273618/b273618.txt">Table of n, a(n) for n = 1..10000</a>
%e A273618 m=131; 131=2*65+1; 3^65 mod 131 = 1 and 65^65 mod 131 = 1.
%p A273618 filter:= proc(n) local k;
%p A273618   k:= (n-1)/2;
%p A273618   3 &^ k mod n = 1 and k &^ k mod n = 1
%p A273618 end proc:
%p A273618 select(filter, [seq(i,i=3..3000, 4)]); # _Robert Israel_, Nov 28 2019
%t A273618 2#+1&/@Select[Range[1,1200,2],PowerMod[3,#,2#+1]==PowerMod[ #,#,2#+1] == 1&] (* _Harvey P. Dale_, May 05 2022 *)
%Y A273618 Subsequence of A176997.
%Y A273618 Cf. A001262, A001567, A107007, A168539, A214151.
%K A273618 nonn
%O A273618 1,1
%A A273618 _Alzhekeyev Ascar M_, May 26 2016