A191030 Primes that are quadratic residues mod 41.

2, 5, 23, 31, 37, 43, 59, 61, 73, 83, 103, 107, 113, 127, 131, 139, 163, 173, 197, 223, 241, 251, 269, 271, 277, 283, 307, 337, 349, 353, 359, 367, 373, 379, 389, 401, 409, 419, 431, 433, 443, 449, 461, 467, 487, 491, 523, 541, 569, 599, 607, 613, 617, 619

Offset: 1

Author

T. D. Noe, May 24 2011

Keywords

• nonn
• easy

Comments

The only difference between A191030 and A038919 is the term A038919(6) = 41. - Zak Seidov, May 24 2013

Due to quadratic reciprocity, p is a square (mod 41) iff 41 is a square (mod p). The notion "quadratic residue" excludes here equality / zero, so 41 is not in this sequence but in A038919, because 41 = 41^2 (mod 41). - M. F. Hasler, Jan 17 2016

Links

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

Crossrefs

Cf. A038919. - Zak Seidov, May 24 2013

Programs

Magma

[p: p in PrimesUpTo(619) | JacobiSymbol(p, 41) eq 1]; // Vincenzo Librandi, Sep 10 2012

Mathematica

Select[Prime[Range[200]], JacobiSymbol[#,41]==1&]

Extensions

Definition adjusted by M. F. Hasler, Jan 19 2016