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A191055 Primes p that have Kronecker symbol (p|93) = 1. 1
7, 11, 17, 19, 23, 29, 53, 67, 83, 89, 97, 103, 109, 137, 157, 163, 167, 179, 193, 197, 211, 239, 251, 263, 269, 283, 307, 347, 349, 353, 373, 379, 383, 389, 397, 401, 421, 439, 449, 461, 491, 509, 541, 547, 557, 569, 577, 587, 607, 641, 647, 661, 677, 691 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
COMMENTS
From Jianing Song, Oct 13 2022: (Start)
Originally erroneously named "Primes that are squares mod 93".
Equivalently, primes p such that kronecker(93,p) = 1.
Rational primes that decompose in the field Q(sqrt(93)).
Primes congruent to 1, 2, 4, 7, 8, 11, 13, 14, 16, 17, 22, 25, 26, 28, 32, 34, 41, 44, 47, 49, 50, 52, 56, 64, 67, 68, 77, 82 modulo 87. (End)
LINKS
MATHEMATICA
Select[Prime[Range[200]], JacobiSymbol[#, 93]==1&]
PROG
(Magma) [p: p in PrimesUpTo(691) | JacobiSymbol(p, 93) eq 1]; // Vincenzo Librandi, Sep 10 2012
(PARI) isA191055(p) == isprime(p) && kronecker(p, 93) == 1 \\ Jianing Song, Oct 13 2022
CROSSREFS
A038981, the sequence of primes that do not remain inert in the field Q(sqrt(93)), is essentially the same.
Cf. A038982 (rational primes that remain inert in the field Q(sqrt(93)))..
Sequence in context: A346991 A038880 A019365 * A078497 A274505 A256567
KEYWORD
nonn,easy
AUTHOR
T. D. Noe, May 25 2011
EXTENSIONS
Definition corrected by Jianing Song, Oct 13 2022
STATUS
approved

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Last modified March 29 04:23 EDT 2024. Contains 371264 sequences. (Running on oeis4.)