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A191084 Primes p that have Kronecker symbol (p|87) = -1. 2

%I #19 Oct 13 2022 13:57:21

%S 5,19,23,31,37,43,53,59,61,71,73,79,83,97,107,127,149,157,163,167,173,

%T 179,193,197,211,227,229,233,239,257,271,281,307,331,337,347,353,367,

%U 379,383,401,409,419,421,431,433,509,521,541,557,577,587,593,601,607

%N Primes p that have Kronecker symbol (p|87) = -1.

%C From _Jianing Song_, Oct 13 2022: (Start)

%C Originally erroneously named "Primes that are not squares mod 87".

%C Equivalently, primes p such that kronecker(-87,p) = -1.

%C Rational primes that remain inert in the field Q(sqrt(-87)).

%C Primes congruent to 5, 10, 19, 20, 23, 31, 35, 37, 38, 40, 43, 46, 53, 55, 59, 61, 62, 65, 70, 71, 73, 74, 76, 79, 80, 83, 85, 86 modulo 87. (End)

%H Vincenzo Librandi, <a href="/A191084/b191084.txt">Table of n, a(n) for n = 1..1000</a>

%H <a href="/index/Pri#primes_decomp_of">Index to sequences related to decomposition of primes in quadratic fields</a>

%t Select[Prime[Range[200]], JacobiSymbol[#,87]==-1&]

%o (Magma) [p: p in PrimesUpTo(607) | JacobiSymbol(p, 87) eq -1]; // _Vincenzo Librandi_, Sep 11 2012

%o (PARI) isA191084(p) == isprime(p) && kronecker(p, 87) == -1 \\ _Jianing Song_, Oct 13 2022

%Y Cf. A191052 (rational primes that decompose in the field Q(sqrt(15)))..

%K nonn,easy

%O 1,1

%A _T. D. Noe_, May 25 2011

%E Definition corrected by _Jianing Song_, Oct 13 2022

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Last modified March 29 09:44 EDT 2024. Contains 371268 sequences. (Running on oeis4.)