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Primes that are not squares mod 163.
3

%I #29 Dec 21 2022 17:22:21

%S 2,3,5,7,11,13,17,19,23,29,31,37,59,67,73,79,89,101,103,107,109,127,

%T 137,139,149,157,181,191,193,211,229,233,239,241,257,269,271,277,283,

%U 293,311,317,331,337,349,353,389,401,431,433,443,449,463,467,479,491,509,521,541

%N Primes that are not squares mod 163.

%C Inert rational primes in Q(sqrt -163). (Note that 41 is not inert in this field, it decomposes - see A296921.)

%D Helmut Hasse, Number Theory, Grundlehren 229, Springer, 1980, page 498.

%H Robert Israel, <a href="/A296915/b296915.txt">Table of n, a(n) for n = 1..10000</a>

%H <a href="https://oeis.org/wiki/Index_to_OEIS:_Section_Pri#primes_decomp_of">Index to sequences related to decomposition of primes in quadratic fields</a>

%p Load the Maple program HH given in A296920. Then run HH(-163,200); - _N. J. A. Sloane_, Dec 26 2017

%o (PARI) lista(nn) = forprime(p=2, nn, if (!issquare(Mod(p, 163)), print1(p, ", "));); \\ _Michel Marcus_, Dec 24 2017

%K nonn

%O 1,1

%A _Ed Pegg Jr_, Dec 22 2017

%E Corrected by _N. J. A. Sloane_, Dec 25 2017 (including deletion of incorrect comments in CROSS-REFERENCES)