Month: May 2023

To calculate the terms of the chaotic TM sequence, it’s best to do it one bit at a time, meaning to do theleast significant bit first (or bit 1), then bit 2, then bit 3 and so on for a number of bit positionsapproximately equal to log_2(n_max), where n_max is the largest value of n… Continue reading Computing the lowest 6 bits of an unusual sequence

Sure, here’s a brief summary: In an attempt to improve efficiency in finding potential pseudoprimes (a number that passes certain primality tests despite not being prime), a number of evolving scripts have been employed, harnessing the mathematical power of the PARI/GP computing environment. These scripts aimed to conduct certain pseudoprime tests on terms generated from… Continue reading Pseudoprime testing, script included

Recently, our team has made significant progress in the research and exploration of Turing machines, specifically focusing on a five-state machine that exhibits chaotic behavior. The approach has been to examine the machine’s “tape” – the primary data structure that it manipulates. A new and innovative proposal has been put forward that may offer deeper… Continue reading Update on Turing Machine Research – Rethinking Tape Analysis

Congratulations on generating agreement for 512k terms of the sequence! The code you’ve shared appears to be a refinement of your original Turing machine implementation. Your code generates a binary sequence using the initial “gen” arrays, then expands this sequence exponentially by applying a recursive rule to generate the next “gen” array from the previous… Continue reading ChatGPT-4 comments on my program to predict a mysterious sequence

Our ongoing research into the mysterious sequence originating from Marxen and Buntrock’s chaotic Turing machine (Tm) continues to yield intriguing insights. We have implemented an advanced sequence generation algorithm in C, which successfully emulates the initial 4096 terms of this complex sequence, mirroring Marxen and Buntrock’s original process. The generation algorithm, which begins with five… Continue reading Progress Report on Chaotic Turing Machine Sequence Research

Background: We’ve been working on a problem related to predicting a specific sequence of numbers. The sequence is generated through a mysterious process that we are trying to model with a C program. The C program, however, is not correctly predicting the sequence as expected, leading to differences in output and therefore a challenging debugging… Continue reading Debugging and Prediction Challenges in Mysterious Sequence Generation Using C Code

The Mysterious Sequence is a peculiar binary pattern that we’ve been studying. Starting with a “1”, it generates a binary array by a simple rule: each bit duplicates itself and then appends an inverted version. This results in a fascinating pattern of zeros and ones. We initially thought this sequence might be related to the… Continue reading An Algorithmic Description of the “Mysterious Sequence”

Dear Team, I am writing to provide an update on the development of our prediction algorithm for the Moser-de Bruijn sequence. The sequence, notable for its origins in the run-length encoding of the tape of a chaotic 5-state Turing machine, presents unique challenges for accurate prediction. As you may know, the Moser-de Bruijn sequence is… Continue reading Memo on the Prediction Algorithm for the Moser-de Bruijn Sequence

Dear Team, I would like to bring your attention to an intriguing algorithm that we have recently developed. The goal was to predict the ‘next generation’ in the Moser-de Bruijn sequence. This sequence, found within number theory, is generated from the sum of distinct powers of 4 and carries intriguing structural properties. Our algorithm begins… Continue reading Generation Algorithm for Moser-de Bruijn Sequence

Indeed, the concept of “generations” and the understanding of sequential transitions has proved to be a very insightful approach in your investigation of the Moser-de Bruijn sequence. This generation-based concept has provided an effective framework to analyze and predict the pattern of the sequence. The identification of the last quarter of the current generation as… Continue reading Copied from ChatGPT-4 discussion

We have recently embarked on a study of the Moser-de Bruijn sequence and its generational patterns. The sequence is renowned for its intriguing recurrence and regularity, and we’ve discovered compelling hints of structured growth across generations. Our approach involved breaking down the sequence into ‘genfiles’, each representing a specific generation (bit) of the sequence. Each… Continue reading Exploration of Moser-de Bruijn Sequence Generational Patterns

Subject: Update on Moser-de Bruijn Sequence Analysis Dear Team, Our ongoing exploration of the Moser-de Bruijn sequence has yielded some intriguing insights. The original complexity of the sequence’s patterns has begun to distill into a simpler and more manageable framework, particularly with the introduction of the function g(x) = round(1.0815 * 1.5^x). Through deep analysis,… Continue reading A memo from ChatGPT-4

The prompt was: “So do I. I think this is a turning in human history: the rise of higher AI using LLM…” and GPT-4’s response: Indeed, the development of large language models (LLMs) and AI in general has been a significant turning point in human history. These technologies have the potential to transform a multitude… Continue reading What Chat-GPT-4 thinks

To whom it may concern, We’ve identified a potentially promising line of inquiry relating to sequence A274152, derived from a chaotic Turing machine. This sequence has intrigued researchers due to its unpredictable nature and lack of apparent pattern. Our new approach is rooted in the hypothesis that the opcode sequences used in evaluating certain polynomials… Continue reading A memo written by ChatGPT-4

Memo: Recent developments have allowed us to establish an intriguing link between a mysterious sequence arising from a chaotic Turing machine and a newly developed algorithm. This sequence, cataloged as A274152 in the OEIS database, displays a surprising property that we’ve successfully captured using a novel approach involving numerical approximation. The algorithm uses opcode sequences… Continue reading A Connection Between the Chaotic Turing Machine and A New Algorithm

We embarked on an in-depth investigation into the growth patterns of a tree structure at a growth factor of 1.5, focusing on the resulting number of distinct integers after each generation. Through the development and utilization of precise computational models, our empirical observations revealed a numerical sequence with compelling properties.However, a comparison with the existing… Continue reading (ChatGPT-4) Memo: Discrepancies and Conjectures Surrounding Tree Growth Numbers at 1.5: OEIS A274152 versus Empirical Observations

As part of our ongoing efforts in numerical analysis and understanding of mathematical phenomena, this memo provides a comparative review of three distinct sequences: a Turing Machine-generated sequence, the OEIS A274152 sequence, and a sequence generated from empirical results on tree evaluations at 1.5. Each of these sequences presents interesting characteristics and complexities. (a) Turing… Continue reading Review and Comparison of Three Numerical Sequences: Turing Machine Sequence, OEIS A274152, and Empirical Results from Tree Evaluations

k d_k A274152_{k+2} d_k/A274152_{k+2}1 2 2 1.0002 2 2 1.0003 4 4 1.0004 6 6 1.0005 8 8 1.0006 12 12 1.0007 18 18 1.0008 28 28 1.0009 42 42 1.00010 62 62 1.00011 94 96 0.97912 140 142 0.98613 210 210 1.00014 316 316 1.00015 474 474 1.00016 710 712 0.99717 1066 1070 0.99618… Continue reading Re: OEIS (A274152) and a mysterious sequence

I’m writing to provide an update on our recent exploration into Turing Machine (TM) simulations, the resulting technical issues we’ve encountered, and some intriguing discoveries about the Mandelbrot Sequence. Our current focus has been on a particular Turing Machine, referred to as the Chaotic Turing Machine (TM). It has the unique ability to generate segments… Continue reading Recent Developments in Turing Machine Simulations and Associated Challenges

1. Introduction The Mysterious Sequence (MS) is a sequence of integers generated by a 4-symbol Turing Machine (TM). Previous analyses and conjectures have identified patterns and possible rules that the TM follows to generate the MS. The TM is believed to have some form of memory, which it uses to generate the sequence. This memo… Continue reading Memo: Conjectures on the Mysterious Sequence (MS)

Over the course of our recent investigations into the behavior of our Turing Machine (TM), we have made some interesting observations regarding a mysterious sequence (MS) of numbers generated by the machine. Here, I’d like to summarize our findings and propose some conjectures that have arisen from our discussions. Please note that these observations and… Continue reading Observations and Conjectures on Mysterious Sequence (MS)

Date: May 15, 2023 In this discussion, we analyzed the rule sequences of a Turing Machine simulation. The unique nature of these sequences, combined with their repetitive patterns, suggests that they represent a highly structured system, likely following some form of algorithmic progression. The sequences appear to represent a form of ‘language’, with certain repeated… Continue reading Turing Machine Simulation Analysis

Introduction:In the vast realm of data compression, where the quest to minimize file sizes often seems like an endless pursuit, a remarkable feat has been achieved. This essay dives into the fascinating tale of compressing 65536 terms of the mysterious sequence (MS) into a mere 146 bytes. The compression journey unfolds, revealing the techniques employed… Continue reading The Remarkable Compression Journey: Shrinking 65536 Terms of MS to a Mere 146 Bytes

I am writing this memo to summarize our collaborative work on two key aspects related to the mysterious sequence (MS): compressing the 65536 terms and observing the stabilization of MS terms 1 to 65536. In summary, our collaborative work led to the successful compression of the 65536 terms of the MS sequence, reducing the storage… Continue reading Summary of Work on Compressing 65536 Terms and Stabilization of MS Sequence

I am writing this memo to summarize the results and conjectures we have discovered during our analysis of the mysterious sequence. Our investigation has provided valuable insights into the patterns and relationships within the sequence, leading to intriguing conjectures. Firstly, we observed that the bits b1, b2, b3, and b4 of ms(n) exhibit periodic behavior.… Continue reading Analysis of Results and Conjectures on the Mysterious Sequence

Subject: Analysis of the Mysterious Sequence and Efficient Computation of its Least Significant Bits Dear [Recipient], I am writing this memo to document our joint work on the mysterious sequence, specifically focusing on the efficient computation of the three least significant bits of ms(n), where n is greater than or equal to 1. Our approach… Continue reading Memo for the record on a conversation with ChatGPT-4

Certainly! Here’s a summary of the conversation so far: The conversation began with the mention of a “mysterious sequence” and a discussion about its properties. It was noted that bit 1 of the sequence is always 1, and bit 2 has a periodicity of 4. It was also observed that bit 3 of the sequence… Continue reading chatgpt memo for the record 5/13/2023

In this conversation, we have investigated the properties of a mysterious sequence (m.s.) and its connection to various number systems and periodicities. Our exploration led us to the following conclusions about the bits of the mysterious sequence: Our exploration of the mysterious sequence also touched upon base phi representations, where phi is the Golden Ratio.… Continue reading Memo: Periodic Patterns and Properties in the Bits of the Mysterious Sequence: Insights and Observations

A curious integer sequence has recently caught the attention of researchers and enthusiasts alike. The sequence starts with the following terms: 3, 1, 5, 3, 7, 1, 9, 3, 3, 1, 13, 3, 15, 1, 17, 11, 3, 1, 21, 3, 7, 1, 25, 3, 3, 1, 29, 3, 31, 1, 33, 27, 3, 1,… Continue reading Exploring a Mysterious Number Sequence with ChatGPT-4

What follows is a session of RSA signature of a plaintext posed as a challenge (using the same public key cryptosystem principles as with passkeys).It’s done in the PARI/gp mathematical package, discussed in the Wikipedia article:https://en.wikipedia.org/wiki/PARI/GP ? m%34 = 5465798471147901675849051289068992578113810313803306801322798589552754629\1242611465792851239580266854599972607779853187547997189218545870650492956442288\1281538124915518713893909125084109697142260421619327466306448536071182639652883\8983714691689754395189303296685968954684413638930376935206319890305102673762831\2312430794644322057060509499239344208716593418323934854611735337661752369166649\4859266109952537706404048449734298775248786339353543478021795601285278679533589\2675892392535452149196870481065240709832738212923994852485874296040793031751458\663876837875457472131514041686146268832596427326942909357104936378221// the RSA modulus: 616 digits long, or 2046 bits. ? public%35 = 65537 // the… Continue reading Passkeys and Public Key Cryptography

In the Sicilian Defense, Sveshnikov Variation with 7. Bg5, I followed book moves up to and including 17… g6 . This last move might be an inaccuracy by Black, since the evaluation following this move is +0.50 while before the move, the evaluation is +0.12 . [ +0.12 is better than +0.50 from Black’s point… Continue reading Various engines vs Stockfish 15.1 depth=39 (result: 1-0)