Math Is Fun Forum

(*  PROGRAM CALCULATING THE SQUARE SUM CHAINS AND TESTING THEIR CIRCULARITY 
     Based on Georgiev's square sum chain creating algoritm                  
     By Krasimir Geogiev
     December, 2005 *)

(*____________________________________________________________*)
(* data *)

n := 17
k := 2

(* /data *)
(*____________________________________________________________*)
(* function defining *)

sq[x_] := If[x^(1/2) == Floor[x^(1/2)], 1, 0]
(* this function gives 1 when x is perfect square and 0 when it isn't. *)

sqcei[x_] := Ceiling[(x+sq[x])^(1/2)]^2
(* this function gives the smallest perfect square which is greater than x. *)

(* /function defining *)
(*____________________________________________________________*)
(* calculations *)
a[1] := k
Do[b[i] = 0, {i, 1, n^3}]
b[k] := 1
Do[
  p = sqcei[a[i - 1]] - a[i - 1];
  j = 0;
  While[j == 0,
    If[b[p] == 0,
      b[p] = 1;
      a[i] = p;
      j = 1,
      p = sqcei[p + a[i - 1]] - a[i - 1]
      ]], {i, 2, n}]
(* /calculations *)
(*____________________________________________________________*)
(* output *)
t=Table[a[i],{i,1,n}]
max = Max[t]
iscir=If[sq[a[n] + k] == 1, 1, 0]
(* /output*)
(*____________________________________________________________*)

(* output *)
Print["The chain:"]
t = Table[a[i], {i, 1, n}]
Print["Length:"]
n
Print["Maximal number:"]
Max[t]
Print["Graphical plot:"]
ListPlot[t, PlotJoined -> True]
isO[x_] := If[sq[a[x] + k] == 1, 1, 0]
Print["if j <= n chain is circular:"]
tt = Table[isO[i], {i, 1, n}]
Print["Graphical plot of the circular test:"]
Plot[isO[Floor[x]], {x, 1, n + 1}]
(* /output*)