Ludic numbers: Difference between revisions

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 }
 </lang>
 {{Output}}
 <pre>
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 Ludic Triplets below 250:
 (1 3 7) (5 7 11) (11 13 17) (23 25 29) (41 43 47) (173 175 179) (221 223 227) (233 235 239)
+</pre>
+=={{header|Pascal}}==
+Inspired by "rotors" of perl 6 .
+Runtime nearly quadratic: maxLudicCnt = 10000 -> 0.04 s =>maxLudicCnt= 100000 -> 4.88 s
+There is much space for improvement.Analog to prime wheels 2,3 -> +2+4,+2+4,+2+4 so only 2 of 6 numbers are to check.
+The rotors can be grouped/listed together in order of their remaining cnt values. <10, <100, < 1000,< 10000 to reduce the checks of a special rotor.
+<lang pascal>program lucid;
+{$IFDEF FPC}
+  {$MODE objFPC}
+{$ENDIF}
+const
+  maxLudicCnt = 2005; //must be > 1
+type
+  tDelta = record
+             dNum : LongInt;
+             dCnt : LongInt;
+           end;
+  tLudicList = array of tDelta;
+procedure getLudic(var Ll:tLudicList);
+var
+  n,LudicCnt,i : NativeUint;
+  isLucid : boolean;
+begin
+  n := 1;
+  // special case 1
+  Ll[0].dNum := 1;
+  LudicCnt := 0;
+  repeat
+    inc(n);
+    isLucid := true;
+    //check if n is 'hit' by a prior ludic number
+    For i := 1 to LudicCnt do
+      with Ll[i] do
+      Begin
+        dec(dCnt);
+        IF dCnt = 0 then
+        Begin
+          dcnt := dNum;
+          isLucid := false;
+          BREAK
+        end;
+      end;
+    // a new ludic number found?
+    If isLucid then
+    Begin
+      inc(LudicCnt);
+      with Ll[LudicCnt] do
+      Begin
+        dNum := n;
+        dCnt := n;
+      end;
+    end;
+  until LudicCnt >= High(LL);
+end;
+procedure  firstN(var Ll:tLudicList;cnt: NativeUint);
+var
+  i : NativeInt;
+Begin
+  writeln('First ',cnt,' ludic numbers:');
+  For i := 0 to cnt-2 do
+    write(Ll[i].dNum,',');
+  writeln(Ll[cnt-1].dNum);
+end;
+procedure triples(var Ll:tLudicList;max: NativeUint);
+var
+  i,
+  chk : NativeInt;
+Begin
+  // special case 1,3,7
+  writeln('Ludic triples below ',max);
+  write('(',ll[0].dNum,',',ll[2].dNum,',',ll[4].dNum,') ');
+  For i := 1 to High(Ll) do
+  Begin
+    chk := ll[i].dNum;
+    If chk> max then
+      break;
+    If (ll[i+2].dNum = chk+6) AND (ll[i+1].dNum = chk+2) then
+      write('(',ll[i].dNum,',',ll[i+1].dNum,',',ll[i+2].dNum,') ');
+  end;
+  writeln;
+  writeln;
+end;
+procedure LastLucid(var Ll:tLudicList;cnt: NativeUint);
+var
+  i : NativeUint;
+Begin
+  IF cnt >= length(Ll) then
+    cnt := High(Ll);
+  i:=  length(Ll);
+  writeln(i-cnt,'.th to ',i,'.th ludic number');
+  For i := High(Ll)-cnt+1 to High(Ll)-1 do
+    write(Ll[i].dNum,',');
+  writeln(Ll[High(Ll)].dNum);
+  writeln;
+end;
+function CountLudic(var Ll:tLudicList;Limit: NativeUint):NativeUint;
+var
+  i : NativeUint;
+Begin
+  result := 0;
+  For i := 0 to High(Ll) do begin
+    IF Ll[i].dnum <= Limit then
+      inc(result)
+    else
+      BREAK;
+end;
+end;
+var
+  LudicList : tLudicList;
+BEGIN
+  setlength(LudicList,maxLudicCnt);
+  getLudic(LudicList);
+  firstN(LudicList,25);
+  writeln('There are ',CountLudic(LudicList,1000),' ludic numbers below 1000');
+  LastLucid(LudicList,5);
+  triples(LudicList,250);//all-> (LudicList,LudicList[High(LudicList)].dNum);
+END.
+(*
+//maxLudicCnt = 100000
+...
+.th to 100000.th ludic numbers
+1561291,1561301,1561307,1561313,1561333
+*)
+</lang>
+{{Output}}
+<pre>
+First 25 ludic numbers:
+,2,3,5,7,11,13,17,23,25,29,37,41,43,47,53,61,67,71,77,83,89,91,97,107
+There are 142 ludic numbers below 1000
+.th to 2005.th ludic number
+,21487,21493,21503,21511
+Ludic triples below 250
+(1,3,7) (5,7,11) (11,13,17) (23,25,29) (41,43,47) (173,175,179) (221,223,227) (233,235,239)
 </pre>