num ← ##.osc num ⍝ Oscillate - probably returns 1. This function expounded by L.Collatz in 1937, illustrates the "cleanness" of the D-function style. B.Thwaites (1996) has offered a £1,100 reward for proving that it terminates for all ⍵>0 and Paul Erdős commented: "Mathematics is not yet ready for such problems." In "Gödel, Escher, Bach:", Douglas Hofstadter defines a natural number (n) to be "Wondrous" if (osc n) terminates. He points out that no-one has yet discovered an "un-wondrous" number. This sequence is also known as the "Hailstone" or "3N+1" sequence. Example: osc¨⍳40 ⍝ (engineer's proof) 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 See also: k6174 m91 Back to: contents Back to: Workspaces