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Taha's 2nd Solution of Collatz Sequence

29 July 2024, Version 2
Working Paper
This content is an early or alternative research output and has not been peer-reviewed by Cambridge University Press at the time of posting.

Abstract

Abstract of Taha's 2nd Solution of Collatz Sequence let Collatz Sequence of (r)=S(r) let Collatz Sequence loop of (r)=lS(r) S(n)={(n/2)=k≤n-1,…,(h) or…},n∈N_even,k,h∈N_+⋯Fact 1 S(n)={(n/2)or (3n+1),…}⇒S(n)⊇S((n/2) or (3n+1) ),n∈N_+⋯Fact 2 ⇒ lS(n)= lS((n/2) or (3n+1) )…Fact 3 Example: S(5)={16,8,4,2,1}⇒ ∴S(5)⊇S(16)⊇S(8)⊇S(4)⊇S(2)⊇ S(1)…Fact 1⇒ lS(5)=lS(16)=lS(8)=lS(4)=lS(2)=lS(1)…Fact 2

Keywords

Collatz
2nd Way Collatz
Unsolved Math
Taha
Number Theory

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Version History

Jul 29, 2024 Version 2

Version Notes

in 3rd line I have misprint N(even), suppose N(+). and I made it shorter and easier to understand.

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License

All Rights Reserved

DOI

10.33774/coe-2024-f4j0z-v2
D O I: 10.33774/coe-2024-f4j0z-v2 [opens in a new tab]

Author’s competing interest statement

The author(s) have declared they have no conflict of interest with regard to this content

Ethics

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