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

1,1

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

Mathematica

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

Prog

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

Crossrefs

Cf. A038919. - Zak Seidov, May 24 2013

Sequence in context: A180535 A038919 A141181 * A233074 A100031 A293213

Adjacent sequences: A191027 A191028 A191029 * A191031 A191032 A191033

Keyword

nonn,easy

Author

T. D. Noe, May 24 2011

Extensions

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

Status

approved