Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the 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