A191049 Primes p that have Kronecker symbol (p|82) = 1.

3, 11, 13, 19, 23, 29, 31, 53, 67, 73, 101, 103, 109, 113, 127, 149, 157, 179, 181, 211, 223, 227, 229, 241, 271, 293, 317, 331, 337, 347, 353, 359, 367, 397, 401, 409, 421, 431, 433, 449, 487, 499, 509, 547, 557, 563, 569, 571, 587, 599, 607, 617, 631, 643

Offset: 1

Author

T. D. Noe, May 25 2011

Keywords

• nonn
• easy

Comments

Originally incorrectly named "primes which are squares mod 82", which is sequence A038919. - M. F. Hasler, Jan 15 2016

Links

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

Crossrefs

Cf. A191017, A191018, A191020, A191023, A191025, A191026, A191028, A191029, A191032, A191034, A191036, A191037, A191040, A191042, A191043, A191046, A191047.

Programs

Magma

[p: p in PrimesUpTo(643) | KroneckerSymbol(p, 82) eq 1]; // Vincenzo Librandi, Sep 11 2012

Mathematica

Select[Prime[Range[200]], JacobiSymbol[#,82]==1&]

PARI

select(p->kronecker(p, 82)==1&&isprime(p), [1..1000]) \\ This is to provide a generic characteristic function ("is_A191049") as 1st arg of select(), there are other ways to produce the sequence more efficiently. - M. F. Hasler, Jan 15 2016

Extensions

Definition corrected (following an observation by David Broadhurst) by M. F. Hasler, Jan 15 2016