This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A316976 #14 Jul 17 2021 11:22:41
%S A316976 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 A316976 160,180,192,240,288,320,360,384,480,576,640,720,960,1152,1440,1920,
%U A316976 2880,5760
%N 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.
%C A316976 These are the numbers k such that A316975(k) = 1.
%C A316976 It is conjectured that this list is finite and limited to the terms given in the DATA section.
%C A316976 All known terms are 5-smooth.
%e A316976 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 A316976 0 1 4 9
%e A316976 +------------
%e A316976 0 | 0 11 8 3
%e A316976 1 | 1 0 9 4
%e A316976 4 | 4 3 0 7
%e A316976 9 | 9 8 5 0
%e A316976 The values 1, 5, 7 and 11 are unique in the above table. Therefore 12 belongs to the list.
%t A316976 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 A316976 Cf. A096008, A316975, A051037.
%K A316976 nonn
%O A316976 1,2
%A A316976 _Arnauld Chevallier_, Jul 17 2018