- #106
JeremyEbert
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- 0
well, since raphie seems to be restricted at the moment, i have to ask, is anyone else following this?
JeremyEbert said:Here is a visual prime pattern:
http://plus.maths.org/content/catching-primes
I have developed one of my own based upon trig, square roots and the harmonic sequence.
Here is an animation/application that shows the formula visually:
http://tubeglow.com/test/Fourier.html
Thoughts? Questions?
dimension10 ,dimension10 said:Wow, but it is rather a hard method. Is it, by any chance, related to the sieve of erasothones?
JeremyEbert said:Here is a visual prime pattern:
http://plus.maths.org/content/catching-primes
I have developed one of my own based upon trig, square roots and the harmonic sequence.
Here is an animation/application that shows the formula visually:
http://tubeglow.com/test/Fourier.html
Thoughts? Questions?
PAllen said:Ok, maybe I'm the first that doesn't see it. In the first link, I see the primes. In the second link I don't see what identifies the primes. Clue me in.
Raphie said:A POSSIBLY RELATED SEQUENCE
Suppose the sum of the digits of prime(n) and prime(n+1) divides prime(n) + prime(n+1). Sequence gives prime(n).
http://oeis.org/A127272
2, 3, 5, 7, 11, 17, 29, 41, 43, 71, 79, 97, 101, 107...
e.g.
(2 + 3)/(2+3) = 1
(3+5)/(3+5) = 1
(5+7)/(5+7) = 1
(7+11)/(7+(1+1)) = 2
(11+13/((1+1)+(1+3)) = 4
(17+19/((1+7)+(1+9)) = 2
(29+31/((2+9)+(3+1)) = 4
(41+43/((4+1) + (4+3)) = 7
(43+47/((4+3)+(4+7)) = 5
(71+73)/((7+1)+(7+3)) = 8
(79+83)/((7+9)+(9+7)) = 5
(97+101)/((9+7)+(1+0+1)) = 11
(101+103)/((1+0+1) + (1+0+3) = 34
(107+109)/((1+0+7)+(1+0+9) = 12
ALSO...
Numbers n such that 1 plus the sum of the first n primes is divisible by n+1.
http://oeis.org/A158682
2, 6, 224, 486, 734, 50046, 142834, 170208, 249654, 316585342, 374788042, 2460457826, 2803329304, 6860334656, 65397031524, 78658228038
002 - 002 = 000 = K_00
012 - 006 = 006 = K_02 (Max)
600 - 224 = 336 = K_10 (Lattice Max known)
924 - 486 = 438 = K_11 (Lattice Max known)
6/(5+1) = 1
42/(6+1) = 6
143100/(224+1) = 636
775304/(486+1) = 1592
Like I said, especially given that these two progressions are ones I came across in the process of writing that last post to you, "hmmmm..."
RELATED PROGRESSIONS
Integer averages of first n noncomposites for some n.
http://oeis.org/A179860
1, 2, 6, 636, 1592, 2574, 292656, 917042, 1108972, 1678508, 3334890730, 3981285760, 28567166356, 32739591796, 83332116034
a(n) is the sum of the first A179859(n) noncomposites.
http://oeis.org/A179861
1, 6, 42, 143100, 775304, 1891890, 14646554832, 130985694070, 188757015148, 419047914740, 1055777525624570390, 1492138298614167680, 70288308055831268412, 91779857115464381780, 571686203669195590338
Numbers n that divide the sum of the first n noncomposites.
http://oeis.org/A179859
1, 3, 7, 225, 487, 735, 50047, 142835, 170209, 249655, 316585343, 374788043, 2460457827, 2803329305, 6860334657
This number, in particular, I find interesting...
142835 = 5*7^2*11*53 = (142857 - par_8) = (142857 - 22)
vs. 1/7 = .142857 (repeating)
Indexing from 0, 142857 is the 24th Kaprekar Number
1, 3, 7 and 225, the 1st 4 terms in that last sequence above == (2^1 - 1)^1, (2^2 - 1)^1, (2^3 - 1)^1, (2^4 - 1)^2.
- RF
A Visual Prime Pattern is a recurring and identifiable visual element or design that is present in a variety of different images or visual media. It can be a shape, color, texture, or any other visual characteristic that is consistently found in a group of images.
A Visual Prime Pattern is identified through a process of visual analysis and comparison. Scientists use software and algorithms to analyze large sets of images and identify common visual elements that occur across multiple images.
The purpose of identifying Visual Prime Patterns is to gain a better understanding of visual information and how it is perceived and processed by the human brain. It can also help in the development of new technologies for image recognition and organization.
Yes, Visual Prime Patterns can also be found in non-visual media such as audio and text. In these cases, they may refer to recurring patterns in sound or language that can be identified through similar analysis techniques.
Visual Prime Patterns can be used in a variety of practical applications, such as in image and video editing, advertising and marketing, and even in the development of artificial intelligence. By understanding how visual elements are perceived and processed, we can create more effective and visually appealing designs and technologies.