%I #4 Aug 03 2022 23:28:03
%S 1,3,4,6,8,14,16,17,22,25,27,28,30,38,40,67,68,74,78,82,102,104,109,
%T 110,112,126,128,132,136,140,160,164,188
%N Numbers k such that A356052(k) = A356056(k).
%C Conjectures:
%C (1) This sequence is finite, with greatest term 188.
%C (2) The set {A356056(k) - A356052(k)}, for k >=1,
%C contains every integer >= -5.
%t z = 1000000;
%t u = Table[Floor[n (Sqrt[2])], {n, 1, z}]; (* A001951 *)
%t u1 = Complement[Range[Max[u]], u]; (* A001952 *)
%t v = Table[Floor[n (1/2 + Sqrt[2])], {n, 1, z}]; (* A137803 *)
%t v1 = Complement[Range[Max[v]], v]; (* A137804 *)
%t t1 = Intersection[u, v]; (* A356052 *)
%t t2 = Table[u[[v[[n]]]], {n, 1, z/2}]; (* A356056 *)
%t length = Min[Length[t1], Length[t2]]
%t t = Take[t2, length] - Take[t1, length];
%t {Min[t], Max[t]}
%t Flatten[Position[t, 0]]
%Y Cf. A001951, A137803, A137803, A137804, A356052, A356056.
%K nonn,fini
%O 1,2
%A _Clark Kimberling_, Jul 26 2022