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DrJavi
DrJavi's Scraps (251)

I can't live a normal life, I'm an engineer

Patreon sketches, January 2021

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by DrJavi
I later went on to casually prove that every integer number N>2 is palindromic in at least base N-1.

Keywords
andromorph 2,920, non binary 1,488, genet 649, geek 618, vagentleman 456, math 186
Details
Type: Picture/Pinup
Published: 5 years, 1 month ago
Rating: General

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27 comments

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Aurawing
5 years, 1 month ago
This is what i call Mind Blow xD
Memprys
5 years, 1 month ago
That is very cool.  
Issarlk
5 years, 1 month ago
In metric it'll happen sooner on the 12th of January.
blackstrike
5 years, 1 month ago
Well, 72:72 isn't palindromic, 72:27 is.
Alfador
5 years, 1 month ago
No, it's not meant to be read as decimal digits there. It's mean to be "numeral representing the quantity 72 in base 166" (the 166 in parentheses after the line is the base). It's a single character, the way hexadecimal A-F represent the quantities 10-15 as single numerals.

So for instance, FF is a palindrome even though 1515 would not be (as well as being a completely different number in the decimal representation).
Alfador
5 years, 1 month ago
If you count unary, you could say >= 2 instead of >. >:3
DrJavi
5 years, 1 month ago
If I counted unary, every number would immediately be palindromic in base 1. :^y I might as well consider single digit numbers as palindromic and use base ∞ but that is cheating.
Alfador
5 years, 1 month ago
That's fair! XD

I guess then the interesting question is, since every* N is palindromic in base N-1 (and represented in that base as "11"), which numbers N are palindromes for at least one base k where 1 < k < N-1? Or for that matter, how MANY of those bases create palindromic representations for a given N? (That way you can have that number of representations possibly be zero and count from there, or just include base N-1 and know the minimum will be 1.)

*for integer N > 2 of course
DrJavi
5 years, 1 month ago
Now that would be fun to research! I wonder if there's a rule to define that.
DanielThomas
5 years, 1 month ago
What language is this in?
DrJavi
5 years, 1 month ago
Python.
Greywin
5 years, 1 month ago
I'll have to see if I can write this in POSH when get into work tomorrow.
DanielThomas
5 years, 1 month ago
Ohhh, no wonder I don't recognize it.  x3;  I'm more used to C# and HTML.
Cubba
5 years, 1 month ago
I feel like I could write a formula to find a palindrome base given a number...
DrJavi
5 years, 1 month ago
You absolutely could, you just have to translate Python to algebraic.
SuperBH
5 years, 1 month ago
Does this mean this Inkbunny submission can now be used as a citation for Mathematical papers?
DrJavi
5 years, 1 month ago
Maybe it does! I doubt "all integers are palindromic" is worth any journal's time, but maybe it has applications I can't think of.
TodNaturlich
5 years, 1 month ago
Every number in its own base is represented by the sequence "10", so that represents 10 in base 10, 2 in base 2, 16 in base 16, etc. The sequence "11" is palindromic, and regardless of base is always 1 unit above the sequence "10". So any number N+1 is represented as "11" in base N. Ergo, any number (greater than 1) has at least the "11" palindromic representation.
DrJavi
5 years, 1 month ago
That is correct, that was the picture description.
Doominator
5 years, 1 month ago
Python is a road to madness. That's why I switched to Java.
DrJavi
5 years, 1 month ago
Python made me quit a job, but my soul was already corrupted by chaos.
CrinkleCorgi
5 years, 1 month ago
I literally have no idea what you just said
DrJavi
5 years, 1 month ago
Numbers numbers numbers programming.
Goldy
5 years ago
Python :3
DrJavi
5 years ago
For when you just want to do it quick and easy.
Goldy
5 years ago
My favorite language too ^^

By the way, fstrings are more convenient to use than format method since python 3.7 ^^
DrJavi
5 years ago
That I didn't know! I'll have to practice with them.
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