Data update

Task/Metallic-ratios/DuckDB/metallic-ratios-1.duckdb

@@ -0,0 +1,5 @@
+create or replace table metals as
+  (select (row_number() over () - 1) as b, name
+   from unnest(
+      ['Platinum', 'Golden', 'Silver', 'Bronze', 'Copper','Nickel', 'Aluminium', 'Iron', 'Tin', 'Lead']
+   ) _(name) );

Task/Metallic-ratios/DuckDB/metallic-ratios-2.duckdb

@@ -0,0 +1,24 @@
+# The Lucas-like function as per the task description
+create or replace function lucas(b, n) as table (
+  with recursive cte as (
+    select 1 as ix, 1::HUGEINT as i, 1::HUGEINT as j
+    union all
+    select
+       ix+1,
+       j as i,
+       i + b*j as j
+    from cte
+    where ix < n)
+  select ix, i
+  from cte
+);
+
+# The successive metallic ratio approximations
+create or replace function metallic_ratio(b, n) as table (
+  select i / (lag(i) over ())
+  from lucas(b,n)
+);
+
+.maxwidth 200
+select b, (select array_agg(i) from lucas(b, 15)) as "lucas-like"
+from range(0, 10) _(b);

Task/Metallic-ratios/DuckDB/metallic-ratios-3.duckdb

@@ -0,0 +1,28 @@
+# ix serves both as a rowid and as the count of the number of
+# iterations required to achieve the corresponding ratio
+create or replace function metallic_ratio_to_quiescence(b) as (
+  with recursive cte as (
+    select
+      -1::HUGEINT as ix,
+       1::HUGEINT as previ,
+       1::HUGEINT as i,
+       1::HUGEINT as j,
+       1::DOUBLE as prevratio,
+       1::DOUBLE as ratio
+    union all
+    select
+       ix+1,
+       i as previ,
+       j as i,
+       i + b*j as j,
+       ratio as prevratio,
+       (i::DOUBLE / previ) as ratio
+    from cte
+    where (ix < 4 or prevratio != ratio)
+  )
+  select last((ix, ratio))
+  from cte
+);
+
+select b, name, metallic_ratio_to_quiescence(b)
+from metals;