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Task/Stern-Brocot-sequence/EchoLisp/stern-brocot-sequence-1.echolisp

@@ -0,0 +1,9 @@
+;; stern (2n ) = stern (n)
+;; stern(2n+1) = stern(n) + stern(n+1)
+
+(define (stern n)
+	(cond
+		(( < n 3) 1)
+		((even? n) (stern (/ n 2)))
+		(else (let ((m (/ (1- n) 2))) (+ (stern m) (stern (1+ m)))))))
+(remember 'stern)

Task/Stern-Brocot-sequence/EchoLisp/stern-brocot-sequence-2.echolisp

@@ -0,0 +1,20 @@
+; generate the sequence and check GCD
+(for ((n 10000))
+    (unless (= (gcd (stern n) (stern (1+ n))) 1) (error "BAD GCD" n)))
+    → #t
+
+;; first items
+(define sterns (cache 'stern))
+(subvector sterns 1 16)
+   → #( 1 1 2 1 3 2 3 1 4 3 5 2 5 3 4)
+
+;; first occurences index
+(for ((i (in-range 1 11))) (write (vector-index i sterns)))
+→  0 3 5 9 11 33 19 21 35 39
+
+;; 100
+(writeln (vector-index 100 sterns))
+→ 1179
+
+(stern 900000) → 446
+(stern 900001) → 2479

Task/Stern-Brocot-sequence/EchoLisp/stern-brocot-sequence-3.echolisp

@@ -0,0 +1,13 @@
+;; grouping
+(for ((i (in-range 2 40 2))) (write (/ (stern i)(stern (1+ i)))))
+→ 1/2 1/3 2/3 1/4 3/5 2/5 3/4 1/5 4/7 3/8 5/7 2/7 5/8 3/7 4/5 1/6 5/9 4/11 7/10
+
+;; computing f(1), f(f(1)), etc.
+(define (f x)
+    (let [(a (/ (- (floor x) -1 (fract x))))]
+    (if (> a 1) (f a) (cons a a))))
+
+(define T (make-stream f 1))
+(for((i 19)) (write (stream-iterate T)))
+
+→  1/2 1/3 2/3 1/4 3/5 2/5 3/4 1/5 4/7 3/8 5/7 2/7 5/8 3/7 4/5 1/6 5/9 4/11 7/10

Task/Stern-Brocot-sequence/Oforth/stern-brocot-sequence.oforth

@@ -0,0 +1,7 @@
+: stern(n)
+| l i |
+   ListBuffer new dup add(1) dup add(1) dup ->l
+   n 1- 2 / loop: i [ l at(i) l at(i 1+) tuck + l add l add ]
+   n 2 mod ifFalse: [ dup removeLast drop ] dup freeze ;
+
+stern(10000) Constant new: Sterns

Task/Stern-Brocot-sequence/Sidef/stern-brocot-sequence.sidef

@@ -0,0 +1,34 @@
+# Declare a function to generate the Stern-Brocot sequence
+func stern_brocot {
+    var list = [1, 1];
+    func {
+        list.append(list[0]+list[1], list[1]);
+        list.shift;
+    }
+}
+
+# Show the first fifteen members of the sequence.
+1..15 -> map(stern_brocot()).join(' ').say;
+
+# Show the (1-based) index of where the numbers 1-to-10 first appears
+# in the sequence, and where the number 100 first appears in the sequence.
+[(1..10)..., 100].each { |i|
+    var index = 1;
+    var generator = stern_brocot();
+    while (generator() != i) {
+        ++index;
+    }
+    say "First occurrence of #{i} is at index #{index}";
+}
+
+# Check that the greatest common divisor of all the two consecutive
+# members of the series up to the 1000th member, is always one.
+var generator = stern_brocot();
+var (a, b) = (generator(), generator());
+{
+    assert_eq(Math.gcd(a, b), 1);
+    a = b;
+    b = generator();
+} * 1000;
+
+say "All GCD's are 1";

Task/Stern-Brocot-sequence/jq/stern-brocot-sequence-1.jq

@@ -0,0 +1,12 @@
+def until(cond; update):
+  def _until:
+    if cond then . else (update | _until) end;
+  try _until catch if .== "break" then empty else . end ;
+
+def gcd(a; b):
+  # subfunction expects [a,b] as input
+  # i.e. a ~ .[0] and b ~ .[1]
+  def rgcd: if .[1] == 0 then .[0]
+         else [.[1], .[0] % .[1]] | rgcd
+         end;
+  [a,b] | rgcd ;

Task/Stern-Brocot-sequence/jq/stern-brocot-sequence-2.jq

@@ -0,0 +1,18 @@
+# If n is non-negative, then A002487(n)
+# generates an array with at least n elements of
+# the A002487 sequence;
+# if n is negative, elements are added until (-n)
+# is found.
+def A002487(n):
+  [0,1]
+  | until(
+      length as $l
+      | if n >= 0 then $l >= n
+        else      .[$l-1] == -n
+	end;
+      length as $l
+      | ($l / 2) as $n
+      | .[$l] = .[$n]
+      | if (.[$l-2] == -n) then .
+        else .[$l + 1] = .[$n] + .[$n+1]
+	end ) ;

Task/Stern-Brocot-sequence/jq/stern-brocot-sequence-3.jq

@@ -0,0 +1,31 @@
+# Generate a stream of n integers beginning with 1,1...
+def stern_brocot(n): A002487(n+1) | .[1:n+1][];
+
+# Return the index (counting from 1) of n in the
+# sequence starting with 1,1,...
+def stern_brocot_index(n):
+  A002487(-n) | length -1 ;
+
+def index_task:
+  (range(1;11), 100) as $i
+  | "index of \($i) is \(stern_brocot_index($i))" ;
+
+def gcd_task:
+  A002487(1000)
+  | . as $A
+  | reduce range(0; length-1) as $i
+      ( [];
+        gcd( $A[$i]; $A[$i+1] ) as $gcd
+        | if $gcd == 1 then . else . +  [$gcd] end)
+  | if length == 0 then "GCDs are all 1"
+    else "GCDs include \(.)" end ;
+
+
+"First 15 integers of the Stern-Brocot sequence",
+"as defined in the task description are:",
+stern_brocot(15),
+"",
+"Using an index origin of 1:",
+index_task,
+"",
+gcd_task

Task/Stern-Brocot-sequence/jq/stern-brocot-sequence-4.jq

@@ -0,0 +1,33 @@
+$ jq -r -n -f stern_brocot.jq
+First 15 integers of the Stern-Brocot sequence
+as defined in the task description are:
+1
+1
+2
+1
+3
+2
+3
+1
+4
+3
+5
+2
+5
+3
+4
+
+Using an index origin of 1:
+index of 1 is 1
+index of 2 is 3
+index of 3 is 5
+index of 4 is 9
+index of 5 is 11
+index of 6 is 33
+index of 7 is 19
+index of 8 is 21
+index of 9 is 35
+index of 10 is 39
+index of 100 is 1179
+
+GCDs are all 1