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Iterations, Wolfram Sequences and Approximate Closed Formulas

2017
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Complex Systems
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Examples of computationally simplifying some sequences of non-negative integers are presented. The reduction might be at the cost of leaving out a set of exceptional inputs of zero or rather small density. Iterations a m m∈ℕ of 2 + x with specific initial values x ∈ -2, 2 are considered. Modulo base-4 normality of 1 π 2 , when x 0 and m is outside a set of density about π 2 ; plus 1 on the exceptional set. Adding the second term of a series for 1 2-a m 1 4 csc 2 π 2 m+2 , it is

doi:10.25088/complexsystems.26.2.97
fatcat:x4lvxcwejbhy5isz63a26ztgoy