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A309024
Inert rational primes in the intersection of all Q(sqrt(-d)) where d is a Heegner number.
1
3167, 8543, 14423, 18191, 22343, 25703, 28871, 35999, 40127, 54647, 73127, 75407, 77591, 80783, 82463, 87071, 89759, 93887, 105167, 112103, 112559, 124823, 127679, 130367, 140423, 143519, 149519, 159431, 170231, 175391, 175727, 186647, 187127
OFFSET
1,1
COMMENTS
These primes stay prime in the rings of integers of all imaginary quadratic fields with unique factorization.
However, none of these are prime, e.g., in Q(sqrt(2)) which indicates that there are no numbers that stay prime in all quadratic fields with unique factorization. - Marc Beutter, Aug 25 2020
Primes p such that A307836(n) = -9 with p = prime(n). - Marc Beutter, Aug 25 2020
LINKS
MATHEMATICA
Table[If[MemberQ[JacobiSymbol[{-1, -2, -3, -7, -11, -19, -43, -67, -163}, k], 1], Unevaluated[Sequence[]], k], {k, Prime@Range@PrimePi[200000]}]
CROSSREFS
Sequence in context: A324678 A068266 A140350 * A217247 A020420 A155484
KEYWORD
nonn
AUTHOR
Marc Beutter, Jul 08 2019
STATUS
approved