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Primes that are quadratic residues mod 41.
3

%I #23 Sep 08 2022 08:45:57

%S 2,5,23,31,37,43,59,61,73,83,103,107,113,127,131,139,163,173,197,223,

%T 241,251,269,271,277,283,307,337,349,353,359,367,373,379,389,401,409,

%U 419,431,433,443,449,461,467,487,491,523,541,569,599,607,613,617,619

%N Primes that are quadratic residues mod 41.

%C The only difference between A191030 and A038919 is the term A038919(6) = 41. - _Zak Seidov_, May 24 2013

%C 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

%H Vincenzo Librandi, <a href="/A191030/b191030.txt">Table of n, a(n) for n = 1..1000</a>

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

%o (Magma) [p: p in PrimesUpTo(619) | JacobiSymbol(p, 41) eq 1]; // _Vincenzo Librandi_, Sep 10 2012

%Y Cf. A038919. - _Zak Seidov_, May 24 2013

%K nonn,easy

%O 1,1

%A _T. D. Noe_, May 24 2011

%E Definition adjusted by _M. F. Hasler_, Jan 19 2016