

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
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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

Marc Beutter, Table of n, a(n) for n = 1..10000


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

Cf. A003173, A307836.
Sequence in context: A324678 A068266 A140350 * A217247 A020420 A155484
Adjacent sequences: A309021 A309022 A309023 * A309025 A309026 A309027


KEYWORD

nonn


AUTHOR

Marc Beutter, Jul 08 2019


STATUS

approved



