|
|
Post by dividavi on Feb 22, 2020 8:53:18 GMT
Years ago I made a great discovery about the number 1006301. I thought this discovery to be on a par with Ramanujin's observation that the number 1729 is the smallest number that can be expressed as two separate sums of integers cubed, i.e. 1729=1^3+12^3=9^3+10^3. Alas for me, I learned that someone else had already realized (and documented) the profound truth that I thought to be my own creation concerning the number 1006301. OK, that was kind of depressing but I soon got over it. Regarding the number 1729, I just learned that Ramanujin had been beaten to the punch by a quarter of a millenium by a French mathematician. Frénicle de Bessy had noted the astonishing characteristic of the number 1729 in the year 1657. So I don't feel so bad. OK, so the question to you here is this: What's so amazingly unique about the number 1006301? I'll give you some rather huge hints to aid you in the process of answering. First of all, 1006301 is a prime number. Secondly, it's part of a series of prime numbers which may be infinite in extent, or maybe not. Thirdly, 1006301 is the first (smallest) number in this probably infinite series. Lastly, the sum of the inverses of the numbers in the series has been proven to be convergent. Enough hints. Define the series. Tell me, what's so unique about 1006301? It's the first of what? |
|
buckyv2
Sophomore
@buckyv2
Posts: 443
|
Post by buckyv2 on Feb 22, 2020 14:06:25 GMT
I sort have a fetish for the number 867-5309; ask for Jenny.
|
|
|
|
Post by Dirty Santa PaulsLaugh on Feb 22, 2020 16:37:14 GMT
Nerd 🚨
|
|
|
|
Post by Catman 猫的主人 on Feb 22, 2020 19:13:12 GMT
Clearly 1006301 is the first and only number with those particular digits in that specific order.
|
|
|
|
Post by FilmFlaneur on Feb 22, 2020 19:35:55 GMT
Is it the text number for the Mormon helpline?
|
|
|
|
Post by caretaker on Feb 22, 2020 20:36:32 GMT
I've never looked into your last hint regarding convergence of the sum of series member inverses...but it appears that you are looking at the lowest member of the pair of prime quadruples (i.e., n up to n+38)
|
|
|
|
Post by dividavi on Feb 22, 2020 22:13:24 GMT
I've never looked into your last hint regarding convergence of the sum of series member inverses...but it appears that you are looking at the lowest member of the pair of prime quadruples (i.e., n up to n+38) Yup, you got it right. Source: oeis.org/A059925A059925 Initial members of two prime quadruples (A007530) with the smallest possible difference of 30.
1006301, 2594951, 3919211, 9600551, 10531061, 108816311, 131445701, 152370731, 157131641, 179028761, 211950251, 255352211, 267587861, 557458631, 685124351, 724491371, 821357651, 871411361, 1030262081, 1103104361COMMENTS Numbers n such that {n, n+2, n+6, n+8, n+30, n+32, n+36, n+38} are all prime. - Charles R Greathouse IV, Jun 18 2013 LINKS Jud McCranie and Sebastian Petzelberger, Table of n, a(n) for n = 1..10000 (first 1238 terms from Jud McCranie) D La Pierre Ballard, Prime Number Quadruplets 30 Apart MATHEMATICA Select[Prime[Range[5582*10^4]], AllTrue[#+{2, 6, 8, 30, 32, 36, 38}, PrimeQ]&] (* The program uses the AllTrue function from Mathematica version 10 *) (* Harvey P. Dale, Mar 13 2019 *) PROG (PARI) is(n)=my(v=[0, 2, 6, 8, 30, 32, 36, 38]); for(i=1, 8, if(!isprime(n+v), return(0))); 1 \\ Charles R Greathouse IV, Jun 18 2013 CROSSREFS Cf. A007530, A256842. Sequence in context: A250683 A065326 A213904 * A065327 A234035 A330519 Adjacent sequences: A059922 A059923 A059924 * A059926 A059927 A059928 AUTHOR Martin Raab, Mar 03 2001
|
|
|
|
Post by Arlon10 on Feb 22, 2020 22:39:48 GMT
What do these two images have in common? 
|
|
|
|
Post by Eva Yojimbo on Feb 23, 2020 13:08:42 GMT
What do these two images have in common? Don't know much about geometry, but I recognize the first as a Sierpinski Triangle. Don't recognize the latter... maybe it's the same concept but for pentagons?
|
|
|
|
Post by Arlon10 on Feb 23, 2020 13:35:52 GMT
What do these two images have in common? Don't know much about geometry, but I recognize the first as a Sierpinski Triangle. Don't recognize the latter... maybe it's the same concept but for pentagons? There are no "wrong" answers. There are however short ones. Here is a very different question, "Where is the golden ratio in either of the images?" I want you to get something right. I really do. Another question, "What is the probability you have Google Image Search?"
|
|
|
|
Post by Eva Yojimbo on Feb 23, 2020 14:14:13 GMT
Don't know much about geometry, but I recognize the first as a Sierpinski Triangle. Don't recognize the latter... maybe it's the same concept but for pentagons? There are no "wrong" answers. There are however short ones. Here is a very different question, "Where is the golden ratio in either of the images?" I want you to get something right. I really do. Another question, "What is the probability you have Google Image Search?" No idea, but this is outside my area of expertise. I'm interested to hear whatever you have to say, though. Again, I, unlike you, am willing to learn when I don't know something.  Pretty sure everyone with access to the internet has Google Image Search... not sure what your point there is.
|
|
|
|
Post by Arlon10 on Feb 23, 2020 14:21:39 GMT
There are no "wrong" answers. There are however short ones. Here is a very different question, "Where is the golden ratio in either of the images?" I want you to get something right. I really do. Another question, "What is the probability you have Google Image Search?" No idea, but this is outside my area of expertise. I'm interested to hear whatever you have to say, though. Again, I, unlike you, am willing to learn when I don't know something. Pretty sure everyone with access to the internet has Google Image Search... not sure what your point there is. I think that one day we will all look back on this and laugh.
|
|
|
|
Post by dividavi on Feb 23, 2020 22:48:20 GMT
What do these two images have in common? 1. They're examples of fractal art 2. They're examples of Sierpinski carpet 3. They're computer generated drawings similar in style to MC Escher illustrations, like his Circle Limit series or Fishes and Scales:   
|
|
|
|
Post by Arlon10 on Feb 23, 2020 23:04:38 GMT
What do these two images have in common? 1. They're examples of fractal art 2. They're examples of Sierpinski carpet 3. They're computer generated drawings similar in style to MC Escher illustrations, like his Circle Limit series or Fishes and Scales: Okay, you know more about this than I do. I think you know where the golden ratio is too, but nice of you to let Eva Yojimbo tell it. I worry about that guy. Have you ever experimented with these? I found lots more interesting things.
|
|
|
|
Post by general313 on Feb 24, 2020 0:53:49 GMT
Don't know much about geometry, but I recognize the first as a Sierpinski Triangle. Don't recognize the latter... maybe it's the same concept but for pentagons? Here is a very different question, "Where is the golden ratio in either of the images?" I know that the golden ratio is well associated with regular pentagons (pentagram, dodecahedron), but are there additional manifestations of the golden ratio in your fractal example?
|
|
|
|
Post by Eva Yojimbo on Feb 24, 2020 1:42:26 GMT
1. They're examples of fractal art 2. They're examples of Sierpinski carpet 3. They're computer generated drawings similar in style to MC Escher illustrations, like his Circle Limit series or Fishes and Scales: Okay, you know more about this than I do. I think you know where the golden ratio is too, but nice of you to let Eva Yojimbo tell it. I worry about that guy. Have you ever experimented with these? I found lots more interesting things. In what sense? I live a pretty comfortable life; a little eccentric, maybe, but nothing to be concerned about... not like I'm gonna go full unabomber or anything. 
|
|
|
|
Post by dividavi on Feb 24, 2020 3:53:56 GMT
1. They're examples of fractal art 2. They're examples of Sierpinski carpet 3. They're computer generated drawings similar in style to MC Escher illustrations, like his Circle Limit series or Fishes and Scales: Okay, you know more about this than I do. I think you know where the golden ratio is too, but nice of you to let Eva Yojimbo tell it. I worry about that guy. Have you ever experimented with these? I found lots more interesting things. I had a very vague recollection of the Golden Ratio and all I remembered was that it described spiral shapes like snail shells, cornucopias and The Yellow Brick Road from the Land of Oz. I went to the Wikipedia article and I recalled that I considered it to be a rather dull constant, not on a par with π or e. I still feel that it's dull. As for Sierpinski carpet, somebody else mentioned it earlier; that's why I used it. Bottom line, I'm scarcely an expert on the subject. Getting back to what's important, here's the development of a Sierpinski carpet:      Here's its 3D equivalent, the Menger sponge:  A Menger Sponge sculpture has been built:  A Menger Sponge construction at the University of Bath:  A religious equivalent called the Jerusalem Cube:  As far as I'm concerned, the following equation - simple, elegant, yet profound - is the most astounding mathematical discovery of the 20th century: π^4+π^5 ≈ e^6
|
|
|
|
Post by Eva Yojimbo on Feb 24, 2020 4:33:09 GMT
Okay, you know more about this than I do. I think you know where the golden ratio is too, but nice of you to let Eva Yojimbo tell it. I worry about that guy. Have you ever experimented with these? I found lots more interesting things. I had a very vague recollection of the Golden Ratio and all I remembered was that it described spiral shapes like snail shells, cornucopias and The Yellow Brick Road from the Land of Oz. I know it mostly from the Fibonacci sequence.
|
|
|
|
Post by Arlon10 on Feb 24, 2020 10:40:44 GMT
Okay, you know more about this than I do. I think you know where the golden ratio is too, but nice of you to let Eva Yojimbo tell it. I worry about that guy. Have you ever experimented with these? I found lots more interesting things. I had a very vague recollection of the Golden Ratio and all I remembered was that it described spiral shapes like snail shells, cornucopias and The Yellow Brick Road from the Land of Oz. I went to the Wikipedia article and I recalled that I considered it to be a rather dull constant, not on a par with π or e. I still feel that it's dull. As for Sierpinski carpet, somebody else mentioned it earlier; that's why I used it. Bottom line, I'm scarcely an expert on the subject. Getting back to what's important, here's the development of a Sierpinski carpet: Here's its 3D equivalent, the Menger sponge: A Menger Sponge sculpture has been built: A Menger Sponge construction at the University of Bath: A religious equivalent called the Jerusalem Cube: As far as I'm concerned, the following equation - simple, elegant, yet profound - is the most astounding mathematical discovery of the 20th century: π^4+π^5 ≈ e^6 That is absolutely cool. Are we in an episode of The Big Bang Theory now? I did not know that about the base of natural logarithms. I think the most practical use of the fibonacci sequence is in the arrangement of leaves on a plant. It ensures the leaves are least likely to block the sun of other leaves. A practical use I do not see of the golden ratio is in monitor aspect ratios. I find it difficult to match the available screen resolutions with any of the several monitors I have. Using the golden ratio would ensure a match. At the moment I'm using 1280 x 768 ratio 1.66666 .... which is close to the golden ratio, the monitor is 1.58 though, so there is some distortion.
|
|
|
|
Post by Toasted Cheese on Feb 24, 2020 11:08:02 GMT
What do these two images have in common? I looked at these the other day and meant to comment. From a simple perspective and what you have asked what they have in common, is the inner shapes are the same as the outer but upside down apex and the dimension of width at the largest area are the same for both outer shapes.
|
|
