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A214151 Numbers n from the set == 5 (mod 6) with the property that 3^((3*n-1)/2) == 3 (mod n) and 2^((n-1)/2) == (n-1) (mod n) 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 from the set == 5 (mod 6) with the property that 3^((3*n-1)/2) == 3 (mod n) and 2^((n-1)/2) == (n-1) (mod n)

%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: 1441091, 3587553971, 4528686251, 23260036451, 47535120323, 61070250323, 90474845819, 143193768587, 162016315907, 173868807611, 180998962187, 238364070323, 285370693931, 298577370323, ...

%C Perhaps this sequence contains all the elements of the sequence A107007 or A168539.

%p isA214151 := proc(n)

%p if (n mod 6 = 5) and modp(2 &^ ((n-1)/2),n) = n-1 and modp(3 &^ ((3*n-1)/2),n) = 3 then

%p true;

%p else

%p false;

%p end if;

%p end proc:

%p for n from 5 by 6 do

%p if isA214151(n) then

%p print(n) ;

%p end if;

%p end do: # _R. J. Mathar_, Jul 20 2012

%o (PARI) for(n=0, 200, b=6*n+5; if(Mod(3, b)^((3*b-1)/2)==3, if(Mod(2, b)^((b-1)/2)==b-1 , print(b))));

%Y Cf. A003629, A006970, A175865.

%K nonn

%O 1,1

%A _Alzhekeyev Ascar M_, Jul 05 2012

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Last modified May 18 08:21 EDT 2021. Contains 343995 sequences. (Running on oeis4.)