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

%I

%S 11,59,83,107,131,179,227,251,347,419,443,467,491,563,587,659,683,827,

%T 947,971,1019,1091,1163,1187,1259,1283,1307,1427,1451,1499,1523,1571,

%U 1619,1667,1787,1811,1907,1931,1979,2003,2027,2099,2243,2267

%N Numbers n = 2*k+1 where k is odd with the property that 3^k mod n == 1 and k^k mod n == 1.

%C All composites in this sequence are 2-pseudoprimes, see A001567, and strong pseudoprimes to base 2, A001262.

%C The subsequence of these composites begins: 143193768587, 440097066011, 1188059560451, 1392770336147, 1640446291859, 2526966350771, 3639120872171, 3989703695867, 4202422108523,....

%C Perhaps this sequence contains all the terms of the sequence A107007 (except 3) or A168539.

%H Robert Israel, <a href="/A273618/b273618.txt">Table of n, a(n) for n = 1..10000</a>

%e n=131; 131=2*65+1; 3^65 mod 131 == 1 and 65^65 mod 131 == 1.

%p filter:= proc(n) local k;

%p k:= (n-1)/2;

%p 3 &^ k mod n = 1 and k &^ k mod n = 1

%p end proc:

%p select(filter, [seq(i,i=3..3000, 4)]); # _Robert Israel_, Nov 28 2019

%Y Cf. A001262, A001567, A107007, A168539, A214151.

%K nonn

%O 1,1

%A _Alzhekeyev Ascar M_, May 26 2016

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Last modified May 7 06:57 EDT 2021. Contains 343636 sequences. (Running on oeis4.)