A191031 - OEIS

A191031

Primes that are squares mod 43.

11, 13, 17, 23, 31, 41, 47, 53, 59, 67, 79, 83, 97, 101, 103, 107, 109, 127, 139, 167, 173, 181, 193, 197, 229, 239, 251, 269, 271, 281, 283, 293, 307, 311, 317, 337, 353, 359, 367, 379, 397, 401, 431, 439, 443, 461, 479, 487, 509, 541, 547, 557, 563, 569

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OFFSET

1,1

COMMENTS

These primes split in O_(Q(sqrt(-43))) (note that 43 ramifies, since it's divisible by -43). For the primes p listed here that are less than 43, note that 4p = 43 + x^2. For example, 4 * 13 = 52 = 43 + 3^2, 4 * 17 = 68 = 43 + 5^2. - Alonso del Arte, Apr 03 2018

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 1..1000

MATHEMATICA

Select[Prime[Range[200]], JacobiSymbol[#, 43] == 1 &]

PROG

(Magma) [p: p in PrimesUpTo(569) | JacobiSymbol(p, 43) eq 1]; // Vincenzo Librandi, Sep 10 2012

(PARI) isok(n) = isprime(n) && issquare(Mod(n, 43)); \\ Michel Marcus, Apr 15 2018

CROSSREFS

Sequence in context: A191023 A078861 A106891 * A106890 A048058 A048059

Adjacent sequences: A191028 A191029 A191030 * A191032 A191033 A191034

KEYWORD

nonn,easy

AUTHOR

T. D. Noe, May 24 2011

STATUS

approved