A136803 Squares mod 257.

0, 1, 2, 4, 8, 9, 11, 13, 15, 16, 17, 18, 21, 22, 23, 25, 26, 29, 30, 31, 32, 34, 35, 36, 42, 44, 46, 49, 50, 52, 57, 58, 59, 60, 61, 62, 64, 67, 68, 70, 72, 73, 79, 81, 84, 88, 89, 92, 95, 98, 99, 100, 104, 111, 113, 114, 116, 117, 118, 120, 121, 122, 123, 124

Offset: 1

Author

T. D. Noe, Jan 22 2008

Keywords

• fini
• full
• easy
• nonn

Comments

Because 257 is a Fermat prime, the complement of this set, A136804, is the set of primitive roots (mod 257).

Links

• Nathaniel Johnston, Table of n, a(n) for n = 1..129 (full sequence)
• OEIS Wiki, Index to sequences related to squares

Crossrefs

Cf. A136804 (nonsquares mod 257), A136805 and A136806 (squares/nonsquares mod 65537).

Programs

Maple

A136803 := {}: for n from 0 to 256 do A136803 := A136803 union {n^2 mod 257}: od: op(sort(convert(A136803,list))); # Nathaniel Johnston, Jun 23 2011

Mathematica

p = 257; Select[Range[0, p - 1], JacobiSymbol[ #, p] == 1 &] (* T. D. Noe *)
Table[Mod[n^2, 257], {n, 0, 65}] (* Alonso del Arte, Feb 14 2013 *)

PARI

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

PARI

A136803=Set([k^2 | k <- [0..256]]%257); \\ M. F. Hasler, Nov 15 2017

PARI

lift(select(issquare,Mod([0..256],257))) \\ M. F. Hasler, Nov 15 2017

Formula

a(n) + a(131-n) = 257 for n>1.