A136804 Nonsquares mod 257.

3, 5, 6, 7, 10, 12, 14, 19, 20, 24, 27, 28, 33, 37, 38, 39, 40, 41, 43, 45, 47, 48, 51, 53, 54, 55, 56, 63, 65, 66, 69, 71, 74, 75, 76, 77, 78, 80, 82, 83, 85, 86, 87, 90, 91, 93, 94, 96, 97, 101, 102, 103, 105, 106, 107, 108, 109, 110, 112, 115, 119, 125, 126

Offset: 1

Author

T. D. Noe, Jan 22 2008

Keywords

• fini
• full
• easy
• nonn

Comments

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

Links

• Nathaniel Johnston, Table of n, a(n) for n = 1..128 (full sequence)
• Index entries for sequences related to squares

Crossrefs

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

Programs

Maple

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

Mathematica

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

PARI

for (n=0, 256, if (! issquare(Mod(n, 257)), print1(n, ", "))) \\ Michel Marcus, Mar 12 2017

PARI

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

Formula

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