Pdf benoit cloitre beyond rowland’s gcd sequence

Benoit Cloitre announced one in this paper, but I don’t think it’s been published. Conjecture 2 is actually very simple to proof, I did so in my bachelor’s thesis . Unfortunately, this is only in German, I can write it up in English if you’re interested.

Benoit Cloitre explored several variations on the sequence, including one that depends on the least common multiple (lcm) rather than the greatest common factor; the lcm sequence is discussed further in a recent paper by Ruiz-Cabello.

Eric Rowland has shown for suitable (and possibly all) n that the sequence a(n)=a(n-1)+gcd(n,a(n-1)) in some sense naturally generates primes, and it appears to belong to a broader class of such recurrences. After surveying the variations of this sequence discovered by Benoit Cloitre and Vladimir Shevelev, we discuss some further generalizations of our own.

Recall that a sequence (Fn) is a divisibility sequence if FrFs whenever r s, and is a strong divisibility sequence if gcd ( F r , F s ) = F gcd ( r , s ) for all r , s 1. Proposition 2.2.

Following an idea of Rowland we give a conjectural way to generate increasing sequences of primes using algorithms involving the gcd. These algorithms seem not so useless for searching primes since it appears we found sometime primes much more greater than the number of required iterations.

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beyond which the stabilized algorithm gives a polynomial with the same degree as that of the exact GCD. The MSSP is the minimal precision at and beyond which the algorithm gives a

“Do the Properties of an S-adic Representation Determine Factor Complexity?” (Abstract, pdf , ps, dvi, tex) Article 13.2.7 Olivier Bordellès and Benoit Cloitre , “An Alternating Sum Involving the Reciprocal of Certain Multiplicative Functions” (Abstract, pdf, ps, dvi, tex) Article 13.6.4: Bakir Farhi, “On the Representation of the Natural Numbers as the Sum of Three Terms of the Sequence

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The Fibonacci Series beginning 0,1,1,… is the only (general) Fibonacci sequence beginning a,b,a+b,… which has all the primes as factors of some number in the series. This was proved by …

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of transformations the transformation sequence for the GCD computation for Ao and Bo, and denote it by (Tl, T2, for some k, where Ti, I i k, is either transformation RA

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PDF Following an idea of Rowland we give a conjectural way to generate increasing sequences of primes using algorithms involving the gcd. These algorithms seem not so useless for searching

2 by the choice of which positions are occupied by the slashes among the d+n−1 possibilities, and this is d + n − 1 n − 1 . In any case, we see that the Hilbert function of R agrees with

As outlined in Benoît Cloître’s preprint [BC21], this construction is ispired from Rowland’s type prime generating sequences which count upwards rather than down to 0, see A106108 and references therein.

This is sequence A135506 in OEIS, and as far as I know, no proof to conjecture 1 has been published. Benoit Cloitre announced one in this paper, but I don’t think it’s been published.

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Authors: Benoit Cloitre (Submitted on 22 Jan 2011) Abstract: Following an idea of Rowland we give a conjectural way to generate increasing sequences of primes using algorithms involving the gcd.

2018-12-09T15:39:16Z http://citeseerx.ist.psu.edu/oai2 oai:CiteSeerX.psu:10.1.1.170.5464 2010-09-08 Thesis: Committee: Foundations of Computational Geometric

Benoit Cloitre Starting from a self-referential and recursive definition of the Kolakoski sequence, we introduce the Kolakoski transforms of words on 2 numbers.

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Companion Sequences Associated to the r-Fibonacci Sequence In this talk, we de ne the r-Lucas sequences of type s. These se- quences constitute a family of companion sequences of the generalized r- Fibonacci sequences. We establish the corresponding Binet formula and evaluate generating functions. Therefore we extend the de nition of V(r;s) n to negative n. Also, we exhibit some …

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A divisor of an integer n, also called a factor of n, is an integer which evenly divides n without leaving a remainder. Example 1.1. 7 is a divisor of 35 because 35=7 = 5.

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(MCP), at and beyond which the modiﬁed “stabilized” al-gorithm follows the same sequence of instructions as that of the original “exact” algorithm. Bounding the MCP of any non-trivial and useful algorithm has remained an open problem. This paper studies the MCP of an algorithm for ﬁnding the GCD of two univariate polynomials based on the QR-factorization. We show that the MCP is

FINDING PRIME NUMBERS: MILLER RABIN AND BEYOND 3 As before, by construction (a m)3s = a3s = an 1 = 1modn: By Fermat, if n is prime and gcd(a;n) = 1; the sequence must end in a 1.

20/07/2008 · In a paper just published in a journal I edit, the Journal of Integer Sequences, Rowland defines his formula and proves it generates only 1’s and primes. (1 is generally not accepted as a prime number, for a variety of reasons .

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Conway’s sequence has many interesting properties and connects with Pascal’s triangle, the Gaussian distribution, Fibonacci numbers, and Catalan numbers. Running time recurrences. Use dynamic programming to compute a table of values T(N), where T(N) is the solution to the following divide-and-conquer recurrence.

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8/08/2008 · “Blending simplicity and mystery, Eric Rowland’s formula is a delightful composition in the music of the primes, one everyone can enjoy,” Jeffrey Shallit recently commented on his “Recursivity” blog. A professor at the University of Waterloo, Shallit is editor of the Journal of Integer Sequences .

732 ROWLAND 450 LENINGRAD (60*N) 400 Z 35(Z 0 . (470N) m ~ ASPENDALE (3O*S) HUANCAYC, (12°S) 250 MONTH Figure ! Monthly average ozone concentrations for …

subclass of our k-automatic sets, in which the possible denominators are restricted to powers of k. Yet another model of automata accepting real numbers was studied in [1, 4, 5, 6].

fact that gcd(n, m) divides the linear co m bination rn + sm for all integers r a nd s. A t this p oint the rea der may ob ject that the 1 s pro duced by a ( n ) − a ( n − 1)

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10 conjectures in additive number theory Benoit Cloitre January 25, 2011 Abstract FollowinganideaofRowland[Row]wegiveaconjecturalwaytogen-erate increasing sequences of primes using “gcd-algorithms”.

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“Blending simplicity and mystery, Eric Rowland’s formula is a delightful composition in the music of the primes, one everyone can enjoy,” Jeffrey Shallit recently commented on his “Recursivity” blog. A professor at the University of Waterloo, Shallit is editor of the Journal of Integer Sequences .

Benoit Cloitre announced a proof in Rowland’s original paper, but hasn’t delivered on his promise as of 2015. One thing that is very easy to prove is that every prime (except for ) is a member of the sequence — a nice fact, given that we have very little knowledge of the values that appear in Rowland’s sequence…

If we ignore the 1’s, then, the Rowland formula starts by generating the primes 5, 3, 11, 3 (again), and 23. The reader can easily program up the formula and find …

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The Euclidean algorithm calculates the greatest common divisor (GCD) of two natural numbers a and b. The greatest common divisor g is the largest natural …

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If a sequence 1, b1 , b2 , · · · is non-negative and logconcave then so is the sequence 1, c1 , c2 , · · · determined by the generating function equation X uj X cn un = exp bj . j n≥0

Review Stratospheric ozone depletion F. Sherwood Rowland1,2,* 1Department of Chemistry, and 2Department of Earth System Science, University of California Irvine,

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From discretizations of lines to gcd computations How to discretize a line in the space? How to compute the gcd of three or more numbers? Integer parameters vs. rational parameters

Primality Testing and Factorization Methods Eli Howey May 27, 2014 Abstract Since the days of Euclid and Eratosthenes, mathematicians have taken a keen interest in nding the nontrivial factors of integers, as well as in nding prime numbers, which have no such factors. Until only recently, however, the problem of factoring numbers had no practical application beyond the advancement of pure

interpret the graph of all possible computations: instead of asking whether there exists a sequence of choices that makes the TM accept, we ask how large is the fraction of choices for which this happens.

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10 conjectures in additive number theory arxiv.org

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beyond which the stabilized algorithm gives a polynomial with the same degree as that of the exact GCD. The MSSP is the minimal precision at and beyond which the algorithm gives a

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(PDF) 10 conjectures in additive number theory