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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) 2
 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 Harvey P. Dale, Table of n, a(n) for n = 1..1000 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 MATHEMATICA Select[Range[5, 2500, 6], PowerMod[3, (3#-1)/2, #]==3&&PowerMod[2, (#-1)/2, #] == #-1&] (* Harvey P. Dale, Mar 14 2022 *) 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 July 2 12:39 EDT 2022. Contains 355004 sequences. (Running on oeis4.)