A309024 Inert rational primes in the intersection of all Q(sqrt(-d)) where d is a Heegner number.

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

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