We publish our first data on the Collatz function for 2^{43112609} – 1 (#5 known megaprime) and two of its odd neighbors located at ±10.

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

We publish further data on the Collatz function for 2^{42643801} – 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:

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

We publish our first data on the Collatz function for 2^{42643801} – 1 (#6 known megaprime) and two of its odd neighbors located at ±12.

# “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.

# 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 2^{37156667} – 1 (#7 known megaprime) and two of its odd neighbors located at ±26.

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

We publish our first data on the Collatz function for 2^{32582657} – 1 (#8 known megaprime) and two of its odd neighbors located at ±71149323674102624414.

# Collatz function data for 10223×2^31172165 + 1 (#9 known megaprime)

We publish our first data on the Collatz function for 10223×2^{31172165} + 1 (#9 known megaprime) and two of its odd neighbors located at ±4.

# Collatz function data for 2^30402457 – 1 (#10 known megaprime)

We publish our first data on the Collatz function for 2^{30402457} – 1 (#10 known megaprime) and two of its odd neighbors located at ±2.

# Sequence of record 288-step delayed palindromes found

On 26 April 2019, Rob van Nobelen discovered the 23-digit number 12000700000025339936491 – the first one that takes record-breaking 288 steps to reach a final 142-digit palindrome. The previous record (261 steps) was set in 2005.

We expanded the found number to a sequence with 19353600 terms in total. This sequence currently includes all known 288-step delayed palindromes.

All results are contributed to OEIS and will be published in due course.

# Collatz function data for 2^25964951 – 1 (#11 known megaprime)

We publish our first data on the Collatz function for 2^25964951 – 1 (#11 known megaprime) and two of its odd neighbors located at ±2. Continue reading

# Collatz function data for 2^24036583 – 1 (#12 known megaprime)

We publish our first data on the Collatz function for 2^24036583 – 1 (#12 known megaprime) and two of its odd neighbors located at ±2. Continue reading

# Collatz function data for 2^20996011 – 1 (#13 known megaprime)

We publish our first data on the Collatz function for 2^20996011 – 1 (#13 known megaprime) and two of its odd neighbors located at ±2. Continue reading

# Collatz function data for 1059094^1048576 + 1 (#14 known megaprime)

We publish our first data on the Collatz function for 1059094^1048576 + 1 (#14 known megaprime) and two of its odd neighbors located at ±4. Continue reading