Gray code and the ± sign sequence when ±f(±f(±f(•••±f(x)•••))) is ordered

A previous note gives a rule for determining the sequence of + and - signs to obtain the ith largest value of +ƒ(±ƒ(±ƒ(··· ±ƒ(x)···))) when ƒ(x) is positive and monotonic [1, p. 46, §2]. Shortly after publication the writer received a letter dated March 9, 1972, from John Murchland, of the Planning & Transport Research & Computation Co. Ltd., London, in which he mentioned that the conversion scheme for obtaining the ± sign sequence from i - 1 happens to be also the standard way of going from a binary number to its Gray code equivalent, when after the conversion every plus sign is replaced by 0 and every minus sign by 1.

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