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A316976 Numbers n such that some of the values (r0-r1+n) mod n for all pairs (r0,r1) of quadratic residues mod n are unique. 0
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

These are the numbers n such that A316975(n) = 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

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Last modified July 9 22:46 EDT 2020. Contains 335570 sequences. (Running on oeis4.)