A136805 Squares mod 65537.

0, 1, 2, 4, 8, 9, 13, 15, 16, 17, 18, 19, 21, 25, 26, 30, 32, 33, 34, 35, 36, 37, 38, 42, 49, 50, 52, 53, 55, 60, 64, 66, 68, 69, 70, 71, 72, 74, 76, 77, 79, 81, 84, 87, 93, 97, 98, 100, 103, 104, 106, 107, 109, 110, 115, 117, 120, 121, 123, 128, 129, 132, 135

Offset: 1

Author

T. D. Noe, Jan 22 2008

Keywords

• fini
• full
• easy
• nonn

Comments

Because 65537 is a Fermat prime, the complement of this set, A136806, is the set of primitive roots (mod 65537).

Links

• Nathaniel Johnston, Table of n, a(n) for n = 1..32769 (full sequence)
• OEIS Wiki, Index to sequences related to squares

Crossrefs

Cf. A136806 (nonsquares mod 65537); A136803 and A136804 ((non)squares mod 257).

Cf. A010379.

Programs

Maple

A136805:={}: for n from 0 to 65536 do A136805 := A136805 union {n^2 mod 65537}: od: l:=sort(convert(A136805,list)): l[1..63]; # Nathaniel Johnston, Jun 23 2011

Mathematica

p = 65537; Select[Range[0, p - 1], JacobiSymbol[#, p] == 1 &]

PARI

A136805=Set([k^2 | k <- [0..2^16]]%65537); \\ M. F. Hasler, Nov 15 2017

Sage

[quadratic_residues(65537)] # Zerinvary Lajos, May 24 2009

Scala

((1: BigInt) to (65537: BigInt)).map(n => (n * n) % 65537).toSet.toSeq.sorted // Alonso del Arte, Dec 17 2019

Formula

a(n) + a(32771 - n) = 65537 for n > 1.