The On-Line Encyclopedia of Integer Sequences (OEIS)

Revisions by Gord Palameta (See also Gord Palameta's wiki page)

(Bold, blue-underlined text is an addition; faded, red-underlined text is a ~~deletion~~.)
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A181777

Number of steps to reach 1 in '3x+1' (or Collatz) problem starting with the n-th Mersenne prime.
(history; published version)

#106 by Gord Palameta at Fri Oct 25 11:17:05 EDT 2024

COMMENTS

It is empirically observed conjectured by Ohira and Watanabe that the values of a(n) fluctuate closely around 13.45 * A000043(n) for all but the smallest elements in large Mersenne primes 2^k-1, the sequence, and they conjecture that this constant is fraction steps/k ~ 2 + 3*log(3)/log(4/3), or approximately 13.4565245. - _Gord Palameta_, Oct 24 2024

Discussion

Fri Nov 08

16:49

OEIS Server: This sequence has not been edited or commented on for a week
yet is not proposed for review.  If it is ready for review, please
visit https://oeis.org/draft/A181777 and click the button that reads
"These changes are ready for review by an OEIS Editor."

Thanks.
  - The OEIS Server

#104 by Gord Palameta at Thu Oct 24 12:02:31 EDT 2024

STATUS

editing

proposed

Discussion

Thu Oct 24

17:32

Kevin Ryde: Gord, why do you change the author's comment and then put it in under your name and in wrong date order?  You really (as in really really) shouldn't change the existing work of others.  You're doing far too much on somebody else's open edit.  Set back to editing for you to rectify.

#103 by Gord Palameta at Thu Oct 24 12:02:18 EDT 2024

COMMENTS

It is empirically observed by Ohira and Watanabe that the values of a(n) fluctuate closely around 13.45 * A000043(n) for all but the smallest elements in the sequence, and they conjecture that this constant is 2 + 3*log(3)/log(4/3), or approximately 13.45652. - Gord Palameta, Oct 24 2024

STATUS

proposed

editing

#102 by Gord Palameta at Thu Oct 24 11:57:52 EDT 2024

STATUS

editing

proposed

#101 by Gord Palameta at Thu Oct 24 11:54:40 EDT 2024

LINKS

Gord Palameta, <a href="/A181777/a181777.txt">Table of a(n)/A000043(n) for n = 1..48</a>

Discussion

Thu Oct 24

11:57

Gord Palameta: Added a-file to illustrate the fluctuation around 13.45 * A000043(n)

#100 by Gord Palameta at Thu Oct 24 11:53:54 EDT 2024

COMMENTS

It is observed by Ohira and Watanabe that the values of a(n) fluctuate closely around 13.45 * A000043(n) for all but the smallest elements in the sequence, and they conjecture that this constant is 2 + 3*log(3)/log(4/3), or approximately 13.45652. - _Gord Palameta_, Oct 24 2024

LINKS

Gord Palameta, <a href="/A181777/a181777.txt">Table of a(n)/A000043(n) for n = 1..48</a>

#99 by Gord Palameta at Thu Oct 24 11:31:45 EDT 2024

COMMENTS

It is conjectured observed by Ohira and Watanabe that the values of a(n) fluctuate closely around 13.45 * A000043(n) for large Mersenne primes 2^k-1, all but the smallest elements in the fraction steps/k ~ sequence, and they conjecture that this constant is 2 + 3*log(3)/log(4/3) , or approximately 13.4545652.

#98 by Gord Palameta at Thu Oct 24 10:58:30 EDT 2024

LINKS

Martin Raab, <a href="/A181777/a181777.gp.txt">PARI program</a>

Perig, <a href="https://github.com/Boutoukoat/Collatz-steps-on-large-numbers">Boutoukoat/Collatz-steps-on-large-numbers</a>

Martin Raab, <a href="/A181777/a181777.gp.txt">PARI program</a>

Discussion

Thu Oct 24

11:10

Gord Palameta: Re-alphabetized as per style guide. The author of the fast Collatz program goes by "Perig" on GitHub (despite the repository being named https://github.com/Boutoukoat), and also goes by Perig on MersenneForum.org (https://www.mersenneforum.org/member/17312-perig).

#97 by Gord Palameta at Thu Oct 24 10:55:01 EDT 2024

COMMENTS

S(M136279841) = 1833585702. - _Gord Palameta_, Roderick MacPhee_, Oct 21 2024

LINKS

GitHub, <a href="https://github.com/Boutoukoat/Collatz-steps-on-large-numbers">Boutoukoat/Collatz-steps-on-large-numbers</a>

Perig, <a href="https://github.com/Boutoukoat/Collatz-steps-on-large-numbers">Boutoukoat/Collatz-steps-on-large-numbers</a>

EXTENSIONS

a(48) from _Gord Palameta_, Roderick MacPhee_, Oct 22 21 2024

STATUS

proposed

editing

#96 by Gord Palameta at Tue Oct 22 13:48:55 EDT 2024

STATUS

editing

proposed

Discussion

Tue Oct 22

18:09

Kevin Ryde: "GitHub" is not the author ...

18:13

Kevin Ryde: About two editing at the same time: yes.  Don't want to jump in on somebody else's edit.  The system doesn't prevent it, but it makes multiple new stuff to review.  Roderick MacPhee was in reporting 1833585702 first?

19:37

Roderick MacPhee: Note: i only got involved because perig won't make an account here and wants sequences: More sequences to add in OEIS ?
2024-10-22, 20:28
Maybe it is possible to add these types of sequence in OEIS . f(xi)/ln(xi) -> constant (?) when i -> large and xi is a geometric sequence (dangerous wording because that would imply that Mersenne numbers are part of a geometric sequence).

$ ./collatz 10^60-1 10^600-1 10^6000-1 10^60000-1 10^600000-1 10^6000000-1 10^60000000-1
f(10^60-1)= 1691, time= 0.024 msecs.
f(10^600-1)= 19292, time= 0.314 msecs.
f(10^6000-1)= 183423, time= 4.053 msecs.
f(10^60000-1)= 1818022, time= 69.450 msecs.
f(10^600000-1)= 18206458, time= 1180.891 msecs.
f(10^6000000-1)= 181313037, time= 21097.600 msecs.
f(10^60000000-1)= 1814372163, time= 331593.300 msecs.

I'm orcing them to check with Neil...