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

We publish our first data on the Collatz function for 10223×231172165 + 1  (#9 known megaprime) and two of its odd neighbors located at ±4.

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

We publish our first data on the Collatz function for 230402457 – 1  (#10 known megaprime) and two of its odd neighbors located at ±2.

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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

Collatz function data for 919444^1048576 + 1 (#15 known megaprime)

We publish our first data on the Collatz function for (919444^1048576 + 1 (#15 known megaprime) and two of its odd neighbors located at ±10. Continue reading

Collatz function data for 168451×2^19375200 + 1 (#16 known megaprime)

We publish our first data on the Collatz function for 168451×2^19375200 + 1 (#16 known megaprime) and its closest 2 odd neighbors. Continue reading

Collatz conjecture test for the Top 16 megaprimes started

We have started to test the Collatz conjecture for the Top 16 megaprimes as well as some of their selected odd neighbors. The results will be published in due course.

Breakthrough Junior Challenge 2019 Video: Chebyshev’s Bias

New 7th sign-changing zone for ∆{24;13,1}(x) in Chebyshev’s bias found

We found the 7th sign-changing zone for for ∆{24;13,1}(x) between 5*1015 and 1016. It starts with 8744052767229817, ends with 8772206355445549 and contains 410687 terms. The results are contributed into 2 OEIS sequences: A295355 and A295356.

Chebyshev’s Bias: 165 Years of History