A316976 Numbers k such that some of the values (r0-r1+k) mod k for all pairs (r0,r1) of quadratic residues mod k are unique.

1, 3, 4, 5, 8, 9, 12, 15, 16, 20, 24, 32, 36, 40, 45, 48, 60, 64, 72, 80, 96, 120, 128, 144, 160, 180, 192, 240, 288, 320, 360, 384, 480, 576, 640, 720, 960, 1152, 1440, 1920, 2880, 5760

Offset

1,2

Comments

These are the numbers k such that A316975(k) = 1.

It is conjectured that this list is finite and limited to the terms given in the DATA section.

All known terms are 5-smooth.

Links

Table of n, a(n) for n=1..42.

Example

The quadratic residues mod 12 are 0, 1, 4 and 9. For each pair (r0,r1) of these quadratic residues, we compute (r0-r1+12) mod 12, leading to:
       0  1  4  9
    +------------
  0 |  0 11  8  3
  1 |  1  0  9  4
  4 |  4  3  0  7
  9 |  9  8  5  0
The values 1, 5, 7 and 11 are unique in the above table. Therefore 12 belongs to the list.

Mathematica

Select[Range[10^3], Function[{n}, Min@ Tally[#][[All, -1]] == 1 &@ Flatten[Mod[#, n] & /@ Outer[Subtract, #, #]] &@ Union@ PowerMod[Range@ n, 2, n]]] (* Michael De Vlieger, Jul 20 2018 *)

Crossrefs

Cf. A096008, A316975, A051037.

Sequence in context: A217288 A212011 A207005 * A256173 A050070 A050590

Adjacent sequences: A316973 A316974 A316975 * A316977 A316978 A316979

Keyword

nonn

Author

Arnauld Chevallier, Jul 17 2018

Status

approved