Mwmbl - 3n+1

https://en.wikipedia.org/wiki/Collatz_conjecture — found via Wikipedia

Collatz conjecture

) , 3 n + 1 if n ≡ 1 ( mod 2 ) . {\displaystyle f(n)={\begin{cases}n/2&{\text{if }}n\equiv 0{\pmod {2}},\\[4px]3n+1&{\text{if }}n\equiv 1{\pmod {2}}

Proof that 22/7 exceeds π 1)^{3n}&=\sum _{j=1}^{3n}(-1)^{3n-j}x^{2j}-\sum _{j=0}^{3n-1}(-1)^{3n-j}x^{2j}\\[6pt]&=\sum _{j=0}^{3n-1}\left((-1)^{3n-(j+1)}x^{2(j+1)}-(-1)^{3n

Pentagonal number 1 ) + 1 = 1 2 n ( 3 n − 1 ) + 1 2 ( 1 − n ) ( 3 ( 1 − n ) − 1 ) {\displaystyle 3n(n-1)+1={\tfrac {1}{2}}n(3n-1)+{\tfrac {1}{2}}(1-n){\bigl (}3(1-n)-1{\bigr

Big O notation 2n2 + 3n + 1 = 2n2 + θ(n) means that 2n2 + 3n + 1 = 2n2 + f(n), where f(n) is some function in the set θ(n). In this case, we let f(n) = 3n + 1, which

Mersenne prime that (b + 1)prime(n) − bprime(n) is prime are 1, 1, 1, 1, 5, 1, 1, 1, 5, 2, 1, 39, 6, 4, 12, 2, 2, 1, 6, 17, 46, 7, 5, 1, 25, 2, 41, 1, 12, 7, 1, 7, 327

Collatz conjecture - Wikipedia Directed graph showing the orbits of small numbers under the Collatz map, skipping even numbers. The Collatz conjecture states that all paths eventually l…

http://www.openproblemgarden.org/op/strange_series — found via Mwmbl

The 3n+1 conjecture | Open Problem Garden

Just last month, July 2014, Schorer published another paper which uses similar methods as from his 2008 paper, claiming again to have proven the conjectu…

http://gist.github.com/them0nk/2554785 — found via Mwmbl

3n+1 Problem: PC/UVa IDs: 110101/100 · GitHub

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http://plus.maths.org/content/tags/3n1-conjecture — found via Mwmbl

3n+1 conjecture | plus.maths.org

3n+1 conjecture "Mathematics is not yet ready for such problems." This is what the mathematician John Conway reportedly said about the Collatz conjecture…

3n+1 conjecture

http://arxiv.org/abs/math/0312309v1 — found via Mwmbl

[math/0312309v1] The Collatz 3n+1 Conjecture is Unprovable

Title:The Collatz 3n+1 Conjecture is Unprovable Abstract: In this paper, we show that any proof of the Collatz $3n+1$ Conjecture must have an infinite nu…

[math/0312309v7] The Collatz 3n+1 Conjecture is Unprovable Title:The Collatz 3n+1 Conjecture is Unprovable Abstract: In this paper, we show that any proof of the Collatz $3n+1$ Conjecture must have an infinite nu…

[math/0312309v6] The Collatz 3n+1 Conjecture is Unprovable Title:The Collatz 3n+1 Conjecture is Unprovable Abstract: In this paper, we show that any proof of the Collatz $3n+1$ Conjecture must have an infinite nu…

[math/0312309v2] The Collatz 3n+1 Conjecture is Unprovable Title:The Collatz 3n+1 Conjecture is Unprovable Abstract: In this paper, we show that any proof of the Collatz $3n+1$ Conjecture must have an infinite nu…

[math/0312309v9] The Collatz 3n+1 Conjecture is Unprovable Title:The Collatz 3n+1 Conjecture is Unprovable Abstract: In this paper, we show that any proof of the Collatz $3n+1$ Conjecture must have an infinite nu…

[math/0312309v5] The Collatz 3n+1 Conjecture is Unprovable Title:The Collatz 3n+1 Conjecture is Unprovable Abstract: In this paper, we show that any proof of the Collatz $3n+1$ Conjecture must have an infinite nu…

[math/0312309v3] The Collatz 3n+1 Conjecture is Unprovable Title:The Collatz 3n+1 Conjecture is Unprovable Abstract: In this paper, we show that any proof of the Collatz $3n+1$ Conjecture must have an infinite nu…

[math/0312309v11] The Collatz 3n+1 Conjecture is Unprovable Title:The Collatz 3n+1 Conjecture is Unprovable Abstract: In this paper, we show that any proof of the Collatz $3n+1$ Conjecture must have an infinite nu…

[math/0312309v18] The Collatz 3n+1 Conjecture is Unprovable Title:The Collatz 3n+1 Conjecture is Unprovable Abstract:In this paper, we show that any proof of the Collatz 3n+1 Conjecture must have an infinite numbe…

[math/0312309v16] The Collatz 3n+1 Conjecture is Unprovable Title:The Collatz 3n+1 Conjecture is Unprovable Abstract: In this paper, we show that any proof of the Collatz 3n+1 Conjecture must have an infinite numb…

[math/0312309v12] The Collatz 3n+1 Conjecture is Unprovable Title:The Collatz 3n+1 Conjecture is Unprovable Abstract: In this paper, we show that any proof of the Collatz $3n+1$ Conjecture must have an infinite nu…

[math/0312309v10] The Collatz 3n+1 Conjecture is Unprovable Title:The Collatz 3n+1 Conjecture is Unprovable Abstract: In this paper, we show that any proof of the Collatz $3n+1$ Conjecture must have an infinite nu…

[math/0312309v13] The Collatz 3n+1 Conjecture is Unprovable Title:The Collatz 3n+1 Conjecture is Unprovable Abstract: In this paper, we show that any proof of the Collatz 3n+1 Conjecture must have an infinite numb…

[math/0312309v14] The Collatz 3n+1 Conjecture is Unprovable Title:The Collatz 3n+1 Conjecture is Unprovable Abstract: In this paper, we show that any proof of the Collatz 3n+1 Conjecture must have an infinite numb…

[math/0312309v15] The Collatz 3n+1 Conjecture is Unprovable Title:The Collatz 3n+1 Conjecture is Unprovable Abstract: In this paper, we show that any proof of the Collatz 3n+1 Conjecture must have an infinite numb…

http://math.stackexchange.com/q/137364 — found via Mwmbl

number theory - Thoughts on the Collatz conjecture; integers add…

I've had a thought about the Collatz conjecture (the 3n+1 problem). Suppose some number, C, diverges under the iteration. We first note that C must be od…

http://blog.racket-lang.org/2012/10/the-3n1-problem.html — found via Mwmbl

The 3n+1 problem

The 3n+1 problem 1Introduction: I’m starting to go through [Programming Challenges: The Programming Contest Training Manual](http://www.amazon.com/exec/o…

https://blog.plover.com//math/3n+1-world.html — found via Mwmbl

The Universe of Discourse : The 3n+1 domain

The second proof depends on the (unproved) fact that lowest-term fractions are unique. This is actually a very strong theorem. It is true in the integers…

http://programmers.stackexchange.com/a/310287 — found via Mwmbl

programming practices - Haskell ways to the 3n+1 problem - Softw…

Basically, you are asked to output the biggest Collatz cycle for numbers between i and j. (Collatz cycle of a number $n$ is the number of steps to eventu…

http://dmoj.ca/problem/collatz — found via Mwmbl

3n+1 - DMOJ: Modern Online Judge

3n+1 Pick a positive integer ~n~. If it is odd, multiply it by three and then add one. Otherwise (if it is even), divide it by two. The positive integer …

https://www.johndcook.com/blog/2017/05/03/the-3n1-problem-and-benfords-law/ — found via Mwmbl

The 3n+1 problem and Benford's law

The 3n+1 problem and Benford’s law This is the third, and last, of a series of posts on Benford’s law, this time looking at a famous open problem in comp…

http://community.schemewiki.org/?3n%2b1 — found via Mwmbl

3n+1

The Collatz conjecture is fairly well known ( one example ). Given a positive integer n , as long as n is greater than 1 repeatedly replace n by 3 n + 1 i…

http://jorisvr.nl/article/3n+1-fpga-vs-cpu — found via Mwmbl

3n+1 iteration: FPGA vs CPU

An algorithm for computational verification of the 3n+1 conjecture is implemented on an FPGA and on a fast 64-bit CPU. The performance of the FPGA is sho…

Computing 3n+1 with an FPGA This project uses FPGAs to test the 3n+1 conjecture for a large range of numbers. Project status Verified numbers up to 101×254 = 1.81×1018 Counterexampl…

http://demonstrations.wolfram.com/3n1Graph/ — found via Mwmbl

3n+1 Graph - Wolfram Demonstrations Project

Connect two successive numbers in such a sequence by an arrow to get a graph. Take all the sequences up to a maximum starting number to get the bigger gr…

3n+1 Flying Saucers - Wolfram Demonstrations Project

http://d-scholarship.pitt.edu/24817/ — found via Mwmbl

The 3n+1 Problem: Scope, History and Results - D-Scholarship@Pi…

The 3n+1 Problem: Scope, History and Results Abstract The 3n+1 problem can be stated in terms of a function on the positive integers: C(n) = n=2 if n is …

http://www.colorado.edu/math/3n1-problem-spring-2021 — found via Mwmbl

The 3n+1 Problem (Spring 2021) | Department of Mathematics | Uni…

Secondary Menu Mobile menu The 3n+1 Problem (Spring 2021) Supervisor: Mike Noyes Description: Take any positive integer. If it is even, divide it by 2. I…

http://mathworld.wolfram.com/3nPlus1Problem.html — found via Mwmbl

3n+1 Problem -- from Wolfram MathWorld

https://groups.io/g/UnsolvedProblems/message/396 — found via Mwmbl

3n+1 Cobweb Graph

Likes Search 3n+1 Cobweb Graph Last year I submitted an example of a Cobweb graph of the 3n+1 problem to the user forum of Graph. For anyone interested i…

https://wcipeg.com/problem/collatz — found via Mwmbl

PEG Judge - 3n+1

3n+1 Pick a positive integer n. If it is odd, multiply it by three and then add one. Otherwise (if it is even), divide it by two. The positive integer ob…

https://cs.uwaterloo.ca/journals/JIS/VOL15/Cox/cox10.html — found via Mwmbl

The 3n+1 Problem: A Probabilistic Approach

The 3n+1 Problem: A Probabilistic Approach The Poisson probability distribution is used to model the number of cycles in the generalized Collatz problem.…

http://www.geogebra.org/m/s5eb2wcy — found via Mwmbl

Collatz 3n+1 Sequence – GeoGebra

Collatz 3n+1 Sequence This applet graphs the "3n + 1" sequence. Start with a value, and if it's even, divide it by two, but if it's odd, multiply by 3 an…