login
A214151
Numbers k from the set == 5 (mod 6) with the property that 3^((3*k-1)/2) == 3 (mod k) and 2^((k-1)/2) == (k-1) (mod k).
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
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 terms of the sequence A107007 or A168539.
LINKS
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 , print1(b, ", "))));
CROSSREFS
Subsequence of A176997.
Sequence in context: A141302 A139872 A165977 * A273618 A168539 A320882
KEYWORD
nonn
AUTHOR
Alzhekeyev Ascar M, Jul 05 2012
STATUS
approved