Here’s a quick one. In 1977 the magazine Popular Computing sought “problem situations for which the computer is the best (if not the only) tool for solution” and proposed the Z-sequence as a candidate “problem situation:”
a1 = a2 = 1 and a_n = |2 a_{n-2} + a_{n-1} – n| for n > 2
Among the Z-sequence’s properties, the magazine staff pointed out that “successive values seem unpredictable; that is, the values jump around, but not too wildly” and “almost every integer appears as a term in the sequence sooner or later, except for a few numbers, such as 245, 449, 569, 575, and 903.”
Write a function to find the index of the first occurrence of k (including the five numbers above) in the Popular Computing Z-sequence.
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