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Forum: Miscellaneous Math 2020-10-20, 14:05
Replies: 0
Views: 601
Posted By a nicol
Visualising the Sieve of Eratosthenes

There is an interesting javascript app here: http://www.divisorplot.com/

This can be used to gain a unique visualisation of how divisors are distributed.

I have compiled some screen grabs of...
Forum: Miscellaneous Math 2020-10-14, 19:32
Replies: 1
Views: 662
Posted By a nicol
Factors for the differences between Mersenne numbers

It seems the differences between all Mersenne numbers have factors via:

a1 = Mersenne exponent
a2 = next Mersenne exponent
b = (a2-a1)/2

(2^a1 * 3) * ((4^b - 1)/3)

For example:
Forum: Miscellaneous Math 2019-04-30, 13:25
Replies: 7
Views: 818
Posted By a nicol
I think : 2^n-1 % 3 = [0, 1, 0, 1, 0, 1, 0,...

I think :

2^n-1 % 3 = [0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1...]
2^n-1 % 4 = [1, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3...]
2^n-1 % 5 = [0, 1, 3, 2, 0, 1, 3, 2, 0, 1, 3, 2, 0, 1...]
2^n-1 %...
Forum: Miscellaneous Math 2019-04-30, 12:47
Replies: 7
Views: 818
Posted By a nicol
2^n-1 mod 7 = 0,1,3,0,1,3,0...?

I posted 2^n-1 % 7 was cyclical first, and the sequence wasn't on the oeis or the forum, but have now noticed the Mersenne numbers mod anything seem to be cyclical.

2^n-1 % 3 = [0, 1, 0, 1, 0, 1,...
Forum: Miscellaneous Math 2017-12-19, 09:53
Replies: 21
Views: 1,895
Posted By a nicol
Thank you, I wasn't aware that table existed...

Thank you, I wasn't aware that table existed (hard to search for).

If S[0]=4 is 14,194,37634.. What is the sequence for S[0]=2/3?
Forum: Miscellaneous Math 2017-12-19, 00:42
Replies: 21
Views: 1,895
Posted By a nicol
Cataloguing novel sequences and coincidental...

Cataloguing novel sequences and coincidental connections is a valid research approach period imo. That is the whole premise of the OEIS.
Forum: Miscellaneous Math 2017-12-19, 00:28
Replies: 21
Views: 1,895
Posted By a nicol
Maybe the answer will become apparent to someone...

Maybe the answer will become apparent to someone in some small part via referencing integer sequences. Certainly the many thousands of published papers that reference the OEIS as a data point think...
Forum: Miscellaneous Math 2017-12-19, 00:20
Replies: 21
Views: 1,895
Posted By a nicol
There's only one method?

There's only one method?
Forum: Miscellaneous Math 2017-12-18, 23:58
Replies: 21
Views: 1,895
Posted By a nicol
Why, mathematically speaking, do these signs vary...

Why, mathematically speaking, do these signs vary depending on the start value? Seems like there's a very large dense class theoretical answer to that. Maybe someone could help simplify the answer...
Forum: Miscellaneous Math 2017-12-18, 19:31
Replies: 21
Views: 1,895
Posted By a nicol
How do you tell if the Lehmer symbol of a LL test...

How do you tell if the Lehmer symbol of a LL test is going to be + or -? Could you mention some of the methods you know for establishing this?
Forum: Miscellaneous Math 2017-12-18, 18:39
Replies: 21
Views: 1,895
Posted By a nicol
Trivial, but not previously explicitly associated...

Trivial, but not previously explicitly associated with the LL test in any material I was able to search out. So worth pointing out, I thought.

There is also the fact that the Lucas Lehmer...
Forum: Miscellaneous Math 2017-12-18, 13:25
Replies: 21
Views: 1,895
Posted By a nicol
Hi, which part were you thinking of checking to...

Hi, which part were you thinking of checking to completion? I don't have the cpu time to run larger LL tests atm unfortunately.

I think these triples exist for all Mersenne numbers, I just...
Forum: Miscellaneous Math 2017-12-17, 18:15
Replies: 21
Views: 1,895
Posted By a nicol
Final Lucas Lehmer residuals and Pythagorean triples

Bas Jansen's phd paper has a table of Lehmer symbols:

https://www.math.leidenuniv.nl/scripties/PhDJansen.pdf

(4,q) [5(+),7(-),13(+),17(-),19(-),31(+),61(+),89(-),107(-),127(+),521(-)]
(10,q)...
Forum: Math 2017-11-15, 19:11
Replies: 3
Views: 2,688
Posted By a nicol
Thank you for your reply CRGreathouse - I tried...

Thank you for your reply CRGreathouse - I tried out the code and it works well.

I'm still stuck on how to get from:

49/4 mod 2^13-1
to
49*2048 mod 2^13-1

I'd be grateful if you could...
Forum: Math 2017-11-13, 16:22
Replies: 3
Views: 2,688
Posted By a nicol
Testing Mersenne Primes with Elliptic Curves

In reference to the paper by Song Y. Yan and Glyn James:
...
Forum: Math 2017-07-22, 11:26
Replies: 2
Views: 1,523
Posted By a nicol
Thank you!

Thank you!
Forum: Math 2017-07-22, 09:08
Replies: 2
Views: 1,523
Posted By a nicol
Do 2^p-1 numbers ever have the same first prime factor?

Looking at the small sample from http://oeis.org/A136030 - Smallest prime factor of composite Mersenne numbers:

[23, 47, 233, 223, 13367, 431, 2351, 6361, 179951, 193707721, 228479, 439, 2687,...
Forum: Math 2017-04-05, 20:16
Replies: 2
Views: 1,397
Posted By a nicol
I did feel that my post looks a little...

I did feel that my post looks a little hyperbolic/crankish when that is all that is happening here. However, I haven't found any other direct references to this sequence on google, google books,...
Forum: Math 2017-04-04, 18:21
Replies: 2
Views: 1,397
Posted By a nicol
Geodesic spheres and Mersenne numbers ending in 1 and 7

I thought this was a fun coincidence and I couldn't see it mentioned elsewhere:

Taking the first differences of the sequence of Mersenne numbers ending only in 7: [127, 2047, 32767, 524287...] and...
Forum: Math 2017-04-01, 16:26
Replies: 4
Views: 1,528
Posted By a nicol
Interesting! Thank you for the info Nick, I...

Interesting! Thank you for the info Nick, I couldn't work out why there were no other apparent references to it.

"These are being accompanied by propositions ('stellingen'). Such propositions...
Forum: Math 2017-04-01, 09:46
Replies: 4
Views: 1,528
Posted By a nicol
Proposition 8 in the summary of Bas Jansen's...

Proposition 8 in the summary of Bas Jansen's paper features a triangle constructed inside another triangle. The summary is in Dutch but this seems to be saying that the outer triangle has twice the...
Forum: Math 2017-03-28, 11:08
Replies: 7
Views: 1,624
Posted By a nicol
Thank you for your responses all. I can get the...

Thank you for your responses all. I can get the right answer now.

Thank you for the correction to the table fivemack: Mathematics of Computation, 1943-1993: A Half-century of Computational...
Forum: Math 2017-03-25, 19:22
Replies: 7
Views: 1,624
Posted By a nicol
Sorry, the array from Lucas' paper is 31 bits,...

Sorry, the array from Lucas' paper is 31 bits, not 127 (but he did prove 2^127 -1 is prime using this method).
Forum: Math 2017-03-25, 09:53
Replies: 7
Views: 1,624
Posted By a nicol
Understanding Lucas' chess board algorithm

I'm trying to understand the chess board algorithm that Lucas used compute the residues of Mersenne numbers.

For example, the calculation of residues for 2^7-1:

Form the sequence of numbers S_n...
Forum: Math 2016-11-05, 14:18
Replies: 1
Views: 1,335
Posted By a nicol
Lucas–Lehmer sequences and Heronian triangles with consecutive side lengths

I noticed this demonstration via Wolfram http://demonstrations.wolfram.com/IntegralGridTrianglesWithConsecutiveSideLengths/

Titled: Integral Grid Triangles with Consecutive Side Lengths

If we...
Showing results 1 to 25 of 25

 
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