Number Theory for Computing
Concrete Math
Hierarchies of Principal Twist-Closed Trios
STACS '98 Proceedings of the 15th Annual Symposium on Theoretical Aspects of Computer Science
Numerical calculation of the density of prime numbers with a given least primitive root
Mathematics of Computation
Refining the hierarchy of blind multicounter languages and twist-closed trios
Information and Computation
Fundamental Number Theory with Applications, Second Edition
Fundamental Number Theory with Applications, Second Edition
Permuting operations on strings and their relation to prime numbers
Discrete Applied Mathematics
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Several ways of interleaving, as studied in theoretical computer science, and some subjects from mathematics can be modeled by length-preserving operations on strings, that only permute the symbol positions in strings. Each such operation X gives rise to a family {X"n}"n"="2 of similar permutations. We call an integer nX-prime if X"n consists of a single cycle of length n (n=2). For some instances of X-such as shuffle, twist, operations based on the Archimedes' spiral and on the Josephus problem-we investigate the distribution of X-primes and of the associated (ordinary) prime numbers, which leads to variations of some well-known conjectures on the density of certain sets of prime numbers.