Journal of Integer Sequences, Vol. 23 (2020), Article 20.4.7

Permutations of N Generated by Left-Right Filling Algorithms


F. M. Dekking
Delft University of Technology
Faculty EEMCS
P. O. Box 5031
2600 GA Delft
The Netherlands

Abstract:

We give an in-depth analysis of an algorithm, introduced by Kimberling in the On-Line Encyclopedia of Integer Sequences, that generates permutations of the natural numbers. It turns out that each example of such a permutation in the Encyclopedia is completely determined by some 3-automatic sequence.

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(Concerned with sequences A026136 A026137 A026138 A026139 A026140 A026141 A026142 A026143 A026144 A026145 A026146 A026166 A026167 A026168 A026169 A026170 A026171 A026172 A026173 A026174 A026175 A026176 A026177 A026178 A026179 A026180 A026181 A026182 A026183 A026184 A026185 A026186 A026187 A026188 A026189 A026190 A026191 A026192 A026193 A026194 A026195 A026196 A026197 A026198 A026199 A026200 A026201 A026202 A026203 A026205 A026206 A026208 A026209 A026210 A026211 A026212 A026213 A026214 A026215 A026216 A026217 A026218 A026219 A026220 A026221 A026222 A026223 A026224 A026225 A026226 A026227 A026228 A026229 A026230 A026231 A026232 A065190 A106036 A116178 A189637.)

Received January 26 2020; revised version received April 4 2020. Published in Journal of Integer Sequences, May 5 2020.

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