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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 (list; graph; refs; listen; history; text; internal format)
 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

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Last modified January 18 17:18 EST 2022. Contains 350455 sequences. (Running on oeis4.)