A316976 - OEIS

%I #14 Jul 17 2021 11:22:41

%S 1,3,4,5,8,9,12,15,16,20,24,32,36,40,45,48,60,64,72,80,96,120,128,144,

%T 160,180,192,240,288,320,360,384,480,576,640,720,960,1152,1440,1920,

%U 2880,5760

%N 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.

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

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

%C All known terms are 5-smooth.

%e 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:

%e        0  1  4  9

%e     +------------

%e   0 |  0 11  8  3

%e   1 |  1  0  9  4

%e   4 |  4  3  0  7

%e   9 |  9  8  5  0

%e The values 1, 5, 7 and 11 are unique in the above table. Therefore 12 belongs to the list.

%t 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 *)

%Y Cf. A096008, A316975, A051037.

%K nonn

%O 1,2

%A _Arnauld Chevallier_, Jul 17 2018