Data Update

Task/Sylvesters-sequence/J/sylvesters-sequence.j

@@ -0,0 +1,12 @@
+   2 ('Sum of reciprocals: ' , ":@:(+/))@:%@:([ echo&>)@:((, 1x + */)@[&_~) 9
+2
+3
+7
+43
+1807
+3263443
+10650056950807
+113423713055421844361000443
+12864938683278671740537145998360961546653259485195807
+165506647324519964198468195444439180017513152706377497841851388766535868639572406808911988131737645185443
+Sum of reciprocals: 27392450308603031423410234291674686281194364367580914627947367941608692026226993634332118404582438634929548737283992369758487974306317730580753883429460344956410077034761330476016739454649828385541500213920805r27392450308603031423410234291674686281194364367580914627947367941608692026226993634332118404582438634929548737283992369758487974306317730580753883429460344956410077034761330476016739454649828385541500213920806

Task/Sylvesters-sequence/Pascal/sylvesters-sequence.pas

@@ -0,0 +1,27 @@
+program SylvesterSeq;
+
+{$mode objfpc}{$H+}
+
+uses SysUtils,
+     UIntX; // in the library IntX4Pascal
+(*
+As noted in the Wikipedia article "Sylvester's sequence", we have
+    1/2 + 1/3 + ... + 1/s[j-1] = (s[j] - 2)/(s[j] - 1),
+so that instead of summing the reciprocals explicitly we can just
+calculate an extra term.
+*)
+var
+  s : UIntX.TIntX; // arbitrarily large integer
+  i : integer;
+begin
+  s := 1;
+  for i := 0 to 9 do begin
+    inc(s);
+    WriteLn( SysUtils.Format( 's[%d] = %s', [i, s.ToString]));
+    s := s*(s - 1);
+  end;
+  WriteLn( 'Sum of reciprocals =');
+  WriteLn( (s - 1).ToString);
+  WriteLn( '/'); // on a separate line for clarity
+  WriteLn( s.ToString);
+end.