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Nonsquares mod 257.
6

%I #22 Nov 17 2017 03:27:16

%S 3,5,6,7,10,12,14,19,20,24,27,28,33,37,38,39,40,41,43,45,47,48,51,53,

%T 54,55,56,63,65,66,69,71,74,75,76,77,78,80,82,83,85,86,87,90,91,93,94,

%U 96,97,101,102,103,105,106,107,108,109,110,112,115,119,125,126

%N Nonsquares mod 257.

%C Because 257 is a Fermat prime, these numbers are all primitive roots (mod 257). Complement of A136803.

%H Nathaniel Johnston, <a href="/A136804/b136804.txt">Table of n, a(n) for n = 1..128</a> (full sequence)

%H <a href="/index/Sq#squares">Index entries for sequences related to squares</a>

%F a(n) + a(129-n) = 257.

%p A136804 := {$(0..256)}: for n from 0 to 256 do A136804 := A136804 minus {n^2 mod 257}: od: op(sort(convert(A136804,list))); # _Nathaniel Johnston_, Jun 23 2011

%t p=257; Select[Range[0,p-1], JacobiSymbol[ #,p]==-1&]

%o (PARI) for (n=0, 256, if (! issquare(Mod(n, 257)), print1(n, ", "))) \\ _Michel Marcus_, Mar 12 2017

%o (PARI) A136804=setminus(S=[0..256],Set([k^2 | k <- S]%257)); \\ _M. F. Hasler_, Nov 15 2017

%Y Cf. A136803 (squares mod 257), A136805 and A136806 (squares/nonsquares mod 65537).

%K fini,full,easy,nonn

%O 1,1

%A _T. D. Noe_, Jan 22 2008