Data commit

Task/Yellowstone-sequence/Jq/yellowstone-sequence-1.jq

@@ -0,0 +1,29 @@
+# jq optimizes the recursive call of _gcd in the following:
+def gcd(a;b):
+  def _gcd:
+    if .[1] != 0 then [.[1], .[0] % .[1]] | _gcd else .[0] end;
+  [a,b] | _gcd ;
+
+# emit the yellowstone sequence as a stream
+def yellowstone:
+  1,2,3,
+  ({ a: [2, 3],                               # the last two items only
+     b: {"1":  true, "2": true, "3" : true},  # a record, to avoid having to save the entire history
+     start: 4 }
+   | foreach range(1; infinite) as $n (.;
+       first(
+          .b as $b
+     	  | .start = first( range(.start;infinite) | select($b[tostring]|not) )
+          | foreach range(.start; infinite) as $i (.;
+              .emit = null
+              | ($i|tostring) as $is
+              | if .b[$is] then .
+              # "a(n) is relatively prime to a(n-1) and is not relatively prime to a(n-2)"
+              elif (gcd($i; .a[1]) == 1) and (gcd($i; .a[0]) > 1)
+              then .emit = $i
+              | .a = [.a[1], $i]
+              | .b[$is] = true
+              else .
+              end;
+              select(.emit)) );
+       .emit ));

Task/Yellowstone-sequence/Jq/yellowstone-sequence-2.jq

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+"The first 30 entries of the Yellowstone permutation:",
+[limit(30;yellowstone)]