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Primes p that have Kronecker symbol (p|82) = 1.
4

%I #13 Sep 08 2022 08:45:57

%S 3,11,13,19,23,29,31,53,67,73,101,103,109,113,127,149,157,179,181,211,

%T 223,227,229,241,271,293,317,331,337,347,353,359,367,397,401,409,421,

%U 431,433,449,487,499,509,547,557,563,569,571,587,599,607,617,631,643

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

%C Originally incorrectly named "primes which are squares mod 82", which is sequence A038919. - _M. F. Hasler_, Jan 15 2016

%H Vincenzo Librandi, <a href="/A191049/b191049.txt">Table of n, a(n) for n = 1..1000</a>

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

%o (Magma) [p: p in PrimesUpTo(643) | KroneckerSymbol(p, 82) eq 1]; // _Vincenzo Librandi_, Sep 11 2012

%o (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

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

%K nonn,easy

%O 1,1

%A _T. D. Noe_, May 25 2011

%E Definition corrected (following an observation by _David Broadhurst_) by _M. F. Hasler_, Jan 15 2016