arXiv subjects

Enrique Navarrete

Publications and source records attributed to Enrique Navarrete.

4 recordsLinked to original sources

arXiv2019

Finding Prime Numbers as Fixed Points of Sequences

In this note we describe a method for finding prime numbers as fixed points of particularly simple sequences. Some basic calculations show that success rates for identifying primes this way are over 99.9%. In particular, it seems that the set of odd primes can be obtained as fixed points of the sequence which we call A(1), the sequence of smallest divisors of triangular numbers, where the divisors are positive numbers that have not yet appeared in the sequence.

math.NT↗

arXiv2017

Generalized K-Shift Forbidden Substrings in Permutations

In this note we continue the analysis of permutations that avoid substrings j(j+k), 1 <= j <= n-k, k < n, as well as substrings j(j+k) (mod n), 1 <= j <= n. In the first case the number of such permutations can be obtained from recursions starting from derangement numbers, while in the (mod n) case the number of permutations depends on whether n is prime, and more generally, on whether n and k are relatively prime.

math.CO↗

arXiv2017

Forbidden Substrings In Circular K-Successions

In this note we define circular k-successions in permutations in one-line notation and count permutations that avoid substrings j(j+k) and j(j+k) (mod n). We also count circular permutations that avoid such substrings, and show that for substrings j(j+k) (mod n), the number of permutations depends on whether n is prime, and more generally, on whether n and k are relatively prime.

math.CO↗

arXiv2016

Forbidden Patterns and the Alternating Derangement Sequence

In this note we count linear arrangements that avoid certain patterns and show their connection to the derangement numbers. We discuss the sequence Dn, which counts linear arrangements that avoid patterns 12, 23, ..., (n-1)n, n1, and show that this sequence almost follows the derangement sequence itself since the number of its odd terms is one more than the derangement numbers while the number of its even terms is one less. We also express the derangement numbers in terms of these and other arrangements.

math.CO↗