A356081 Numbers k such that A356052(k) = A356056(k).

1, 3, 4, 6, 8, 14, 16, 17, 22, 25, 27, 28, 30, 38, 40, 67, 68, 74, 78, 82, 102, 104, 109, 110, 112, 126, 128, 132, 136, 140, 160, 164, 188

Offset: 1

Author

Clark Kimberling, Jul 26 2022

Keywords

• nonn
• fini

Comments

Conjectures:

(1) This sequence is finite, with greatest term 188.

(2) The set {A356056(k) - A356052(k)}, for k >=1,

contains every integer >= -5.

Crossrefs

Cf. A001951, A137803, A137803, A137804, A356052, A356056.

Programs

Mathematica

z = 1000000;
u = Table[Floor[n (Sqrt[2])], {n, 1, z}];   (* A001951 *)
u1 = Complement[Range[Max[u]], u];     (* A001952 *)
v = Table[Floor[n (1/2 + Sqrt[2])], {n, 1, z}]; (* A137803 *)
v1 = Complement[Range[Max[v]], v];   (* A137804 *)
t1 = Intersection[u, v];      (* A356052 *)
t2 = Table[u[[v[[n]]]], {n, 1, z/2}];  (* A356056 *)
length = Min[Length[t1], Length[t2]]
t = Take[t2, length] - Take[t1, length];
{Min[t], Max[t]}
Flatten[Position[t, 0]]