Initial data commit

Task/Yellowstone-sequence/J/yellowstone-sequence-1.j

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+Until=: 2 :'u^:(0-:v)^:_'
+assert 44 -: >:Until(>&43) 32  NB. increment until exceeding 43
+gcd=: +.
+coprime=: 1 = gcd
+prepare=:1 2 3"_   NB. start with the vector 1 2 3
+condition=: 0 1 -: (coprime _2&{.)   NB. trial coprime most recent 2,  nay and yay
+append=: ,      NB. concatenate
+novel=: -.@e.   NB. x is not a member of y
+term=: >:@:]Until((condition *. novel)~) 4:
+ys=: (append term)@]^:(0 >. _3+[) prepare
+assert (ys 30) -: 1 2 3 4 9 8 15 14 5 6 25 12 35 16 7 10 21 20 27 22 39 11 13 33 26 45 28 51 32 17

Task/Yellowstone-sequence/J/yellowstone-sequence-2.j

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+GCD=: +.
+relatively_prime=: 1 = GCD
+
+yellowstone=: {{
+  s=. 1 2 3            NB. initial sequence
+  while. y > # s do.
+    z=. <./(1+s)-.s    NB. lowest positive inteeger not in sequence
+    while. if. 0 1 -: z relatively_prime _2{.s do. z e. s end. do.
+      z=. z+1
+    end.   NB. find next value for sequence
+    s=. s, z
+  end.
+}}