No runs of K consecutive tails in N coin tosses

For my Probability and Statistics classes I wrote a small application that solves an old and  well-known problem: “What is the probability that no runs of K consecutive tails will occur in N coin tosses?”

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“Chebyshev’s Bias Visualizer” to be released soon

We are at the final stage of development for “Chebyshev’s Bias Visualizer”, a computer program that allows to visualize Chebyshev’s Bias, the phenomenon closely related to the Generalized Riemann Hypothesis.

The program is capable of producing graphs for any prime number race at required resolution level and save data for the future analysis and use with other graph and data analysis software.

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Collatz function data for 2^82589933 – 1 (#1 known megaprime)

We publish our first data on the Collatz function for 282589933 – 1  (#1 known megaprime) and two of its odd neighbors located at ±2.

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Collatz function data for 2^77232917 – 1 (#2 known megaprime)

We publish our first data on the Collatz function for 277232917 – 1  (#2 known megaprime) and two of its odd neighbors located at ±4.

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Collatz function data for 2^74207281 – 1 (#3 known megaprime)

We publish our first data on the Collatz function for 274207281 – 1  (#3 known megaprime) and two of its odd neighbors located at ±6.

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Collatz function data for 2^57885161 – 1 (#4 known megaprime)

We publish our first data on the Collatz function for 257885161 – 1  (#4 known megaprime) and two of its odd neighbors located at ±8.

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“Easy Rule 30” updated

Our “Easy Rule 30” was updated. You can download updated version through the following links:

Windows 64-bit version

Windows 32-bit version

Linux 64-bit version

MacOS 32/64-bit version

Collatz function data for 2^43112609 – 1 (#5 known megaprime)

We publish our first data on the Collatz function for 243112609 – 1  (#5 known megaprime) and two of its odd neighbors located at ±10.

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Additional Collatz function data for 2^42643801 – 1 (#6 known megaprime)

We publish further data on the Collatz function for 242643801 – 1  (#6 known megaprime) and two of its odd neighbors located at ±12.

Once the maximum is reached, the speed of decline for the log of the Collatz  function seems to be the same for all tested numbers and is equal to approximately -0.096.

“Easy Rule 30” available for download

Our “Easy Rule 30” has become available for download.

Please, use the following links to download:

Windows 64-bit version

Windows 32-bit version

Linux 64-bit version

MacOS 32/64-bit version

Collatz function data for 2^42643801 – 1 (#6 known megaprime)

We publish our first data on the Collatz function for 242643801 – 1  (#6 known megaprime) and two of its odd neighbors located at ±12.

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“Easy Rule 30” software developed

On October 1, 2019 a well-known American mathematician Stephen Wolfram announced “Wolfram Rule 30 Prizes” science competition.

The competition is devoted to the solution of the so-called “Rule 30” – one of the unsolved math problems from a cellular automaton area.

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Sequence of 19353600 record 288-step delayed palindromes published

Our sequence of 19353600 record 288-step delayed palindromes is published as A326414 .

The sequence starts with 12000700000025339936491 (the number discovered by Rob van Nobelen on April 26, 2019), ends with 29463993352000000700020 and contains all terms known at present.

Collatz function data for 2^37156667 – 1 (#7 known megaprime)

We publish our first data on the Collatz function for 237156667 – 1  (#7 known megaprime) and two of its odd neighbors located at ±26.

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Collatz function data for 2^32582657 – 1 (#8 known megaprime)

We publish our first data on the Collatz function for 232582657 – 1  (#8 known megaprime) and two of its odd neighbors located at ±71149323674102624414.

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