Stairs to Heaven...!
June-17, 2011.
It was the birthday of Miss Sinda & Dinsa, my dear friends at the office...
Apart frem being identical twins their names are anagrams of each other, & their b'day is a Prime (17) , with their star-sign's constellation being Gemini which also stands fer twins..!! This really made me ponder & smile a bit..
June-15, 2011.
Another good friend of mine Amod Pandey, had posted a pic of him completing a marathon in the city of Bangalore. But due to heavy work at the office, I hadn't noticed it at till, late in the night of June-17, 2011(Friday), while was doing some official work at home, I just see it...& smile...!
...but was feeling a bit feverish & dizzy.
The number on his shirt, caught my attention---3649.
Well, suffice it to say that it drove my impending sleep away, as I began to find patterns in it, & ask my-self a barrage of questions like what is the smallest number with such a pattern, etc...!
June 18, 2011.
Sunday. Got reminded by mom that it was Fathers' day !
By now, I had devised a series of numbers with such a pattern...as I saw last night.
I secretly wanted to gift my Pappa something he'll feel happy about--because, he's always stressed the importance of Math ever since I was a child.
And the previous night, I had also submitted my series of numbers to an extensive online search program which would apply all kinds of heuristics & algorithms to check & ensure if this series that I had stumbled upon, was indeed a NEW one, or else the proverbial, old-wine in a new bottle...! Luckily, I received confirmation that the series was indeed NEW..!
Along with this confirmation came the need for lots of formalities---I was asked to fill detailed forms about myself, & provide description about the series, & even give a program to compute the first 'n' terms of the series...[Else, anyone could reel off some random numbers & name the resulting series fer him/her-self... :)) ]
Anyways, I did that, & was asked to make some subtle changes in my documentation, which I did too.
The series I had submitted was now in the 'proposed' state---awaiting detailed analysis by REAL mathematicians & scientists behind the Online Encyclopedia of Integer Sequences, who would take the final decision...
Anyway, I immediately fergot all about it---and with absolutely no expectations about it, went to sleep....
The next morning, at office, I was very pleased to find a mail stating that my series had indeed been APPROVED & ALLOCATED...!!!
My lit'l Discovery had changed its status frem PROPOSED to APPROVED...!!
Mine is the 1,91,867'th series 'registered'---though it is actually a kind of generating function for an infinite(?) number of new similar series...! [I only considered n=2 fer now, since the square has always had mysterious applications w.r.t. the Universe around us...!]
That said, there are TONS of questions to be explored like the following :
a) The beautiful stair-case-like graph(s) of the members of this series...
Click on the below graph if you want to see a sample..! :)
{ Notice the unusual structures on the graph ?? Well, i purposely strove hard to make it look like the stamen (with those peculiar anthers !)of a Hibiscus flower ! :-) How ?? By using the Greek small letter 'theta' as the plot 'marker'...! ;)) }
b) Is the series INFINITE...???? Fer ANY value of n ??
[My conjecture is that it IS...at-least fer n=2]
c) Any 'weird' places where this series 'pops-up'...??
Well, those r interesting points to ponder about....
And the below lines express my feelings very aptly..
Love & Best Wishes,
June-17, 2011.
It was the birthday of Miss Sinda & Dinsa, my dear friends at the office...
Apart frem being identical twins their names are anagrams of each other, & their b'day is a Prime (17) , with their star-sign's constellation being Gemini which also stands fer twins..!! This really made me ponder & smile a bit..
June-15, 2011.
Another good friend of mine Amod Pandey, had posted a pic of him completing a marathon in the city of Bangalore. But due to heavy work at the office, I hadn't noticed it at till, late in the night of June-17, 2011(Friday), while was doing some official work at home, I just see it...& smile...!
...but was feeling a bit feverish & dizzy.
The number on his shirt, caught my attention---3649.
Well, suffice it to say that it drove my impending sleep away, as I began to find patterns in it, & ask my-self a barrage of questions like what is the smallest number with such a pattern, etc...!
June 18, 2011.
Sunday. Got reminded by mom that it was Fathers' day !
By now, I had devised a series of numbers with such a pattern...as I saw last night.
I secretly wanted to gift my Pappa something he'll feel happy about--because, he's always stressed the importance of Math ever since I was a child.
And the previous night, I had also submitted my series of numbers to an extensive online search program which would apply all kinds of heuristics & algorithms to check & ensure if this series that I had stumbled upon, was indeed a NEW one, or else the proverbial, old-wine in a new bottle...! Luckily, I received confirmation that the series was indeed NEW..!
Along with this confirmation came the need for lots of formalities---I was asked to fill detailed forms about myself, & provide description about the series, & even give a program to compute the first 'n' terms of the series...[Else, anyone could reel off some random numbers & name the resulting series fer him/her-self... :)) ]
Anyways, I did that, & was asked to make some subtle changes in my documentation, which I did too.
The series I had submitted was now in the 'proposed' state---awaiting detailed analysis by REAL mathematicians & scientists behind the Online Encyclopedia of Integer Sequences, who would take the final decision...
Anyway, I immediately fergot all about it---and with absolutely no expectations about it, went to sleep....
The next morning, at office, I was very pleased to find a mail stating that my series had indeed been APPROVED & ALLOCATED...!!!
My lit'l Discovery had changed its status frem PROPOSED to APPROVED...!!
Mine is the 1,91,867'th series 'registered'---though it is actually a kind of generating function for an infinite(?) number of new similar series...! [I only considered n=2 fer now, since the square has always had mysterious applications w.r.t. the Universe around us...!]
That said, there are TONS of questions to be explored like the following :
a) The beautiful stair-case-like graph(s) of the members of this series...
Click on the below graph if you want to see a sample..! :)
{ Notice the unusual structures on the graph ?? Well, i purposely strove hard to make it look like the stamen (with those peculiar anthers !)of a Hibiscus flower ! :-) How ?? By using the Greek small letter 'theta' as the plot 'marker'...! ;)) }
b) Is the series INFINITE...???? Fer ANY value of n ??
[My conjecture is that it IS...at-least fer n=2]
c) Any 'weird' places where this series 'pops-up'...??
Well, those r interesting points to ponder about....
And the below lines express my feelings very aptly..
Love & Best Wishes,
