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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
11, 59, 83, 107, 131, 179, 227, 251, 347, 419, 443, 467, 491, 563, 587, 659, 683, 827, 947, 971, 1019, 1091, 1163, 1187, 1259, 1283, 1307, 1427, 1451, 1499, 1523, 1571, 1619, 1667, 1787, 1811, 1907, 1931, 1979, 2003, 2027, 2099, 2243, 2267 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

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

The subsequence of these composites begins: 1441091, 3587553971, 4528686251, 23260036451, 47535120323, 61070250323, 90474845819, 143193768587, 162016315907, 173868807611, 180998962187, 238364070323, 285370693931, 298577370323, ...

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

LINKS

Table of n, a(n) for n=1..44.

MAPLE

isA214151 := proc(n)

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

        true;

    else

        false;

    end if;

end proc:

for n from 5 by 6 do

    if isA214151(n) then

        print(n) ;

    end if;

end do: # R. J. Mathar, Jul 20 2012

PROG

(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))));

CROSSREFS

Cf. A003629, A006970, A175865.

Sequence in context: A141302 A139872 A165977 * A273618 A168539 A320882

Adjacent sequences:  A214148 A214149 A214150 * A214152 A214153 A214154

KEYWORD

nonn

AUTHOR

Alzhekeyev Ascar M, Jul 05 2012

STATUS

approved

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Last modified April 19 10:30 EDT 2021. Contains 343112 sequences. (Running on oeis4.)