10 papers
Almost Golomb Sequences
Benoit Cloitre, Gandhar Joshi
Golomb's sequence is the unique nondecreasing sequence of positive integers in which each appears exactly times. It satisfies the global self-referential rule $…
The Golden Sieve
Benoit Cloitre
We revisit the golden sieve, a self-referential deletion process on increasing sequences of positive integers introduced by the author in 2002. Applied to the natural numbers, the…
The holonomic triangle: from a symmetry between and to additive Gamma functions
Benoit Cloitre
Two linear recurrences exhibit mirror symmetry connecting the constants and . When parametrized, their asymptotic connection constants extend to meromorphic functions satisf…
Primes in LCM recurrences
Benoit Cloitre
We study an LCM-based analogue of Rowland's GCD-based prime-generating recurrence, introduced by the author in 2008. The multiplicative increments of this sequence are conjectured…
On a BBP-type formula for in the golden ratio base
Benoit Cloitre
This paper presents a detailed, self-contained proof of a BBP-type formula for expressed in the golden ratio base, . The formula was discovered empirically by the author i…
An effective analytic recurrence for prime numbers
Benoit Cloitre
The Golomb--Keller formula expresses the next prime as a recurrence relation in terms of the first primes using the Riemann zeta function and an Eu…
A study of a family of self-referential sequences
Benoit Cloitre
We introduce and analyze a three-parameter family of self-referential integer sequences : starting from , each term advances by when the index has already…
A BBP-type formula for the remainder of the Madhava-Gregory-Leibniz series
Benoit Cloitre
We derive a BBP-type formula for the remainder of the Madhava-Gregory-Leibniz series for . The result is a closed form in base- with Pochhammer denominators. The analogous f…
On a Family of Nested Recurrences and Their Arithmetical Solutions
Benoit Cloitre
A family of nested recurrence relations , parameterized by an integer with initial condition , is studied. We prove that $…
On the Orthorecursive Expansion of Unity
Benoit Cloitre
The orthorecursive expansion of unity with respect to the system in produces a sequence of rational coefficients defined by an explic…