2023 in Base 37

01062023, 12:21 PM
(This post was last modified: 01062023 12:22 PM by Joe Horn.)
Post: #1




2023 in Base 37
New Year's trivia: 2023 in base 10 equals 1HP in base 37. Posted in the "Not Remotely" forum because no member here has only 1HP.
<0ɸ0> Joe 

01062023, 12:58 PM
(This post was last modified: 01062023 07:52 PM by pier4r.)
Post: #2




RE: 2023 in Base 37
Nice bit of trivia!
An extension would be: find the decimal numbers (and the transforming base) in which one can write HP35, HP71, HP50G and so on. I believe the base 37 would suffice in most cases. Wikis are great, Contribute :) 

01062023, 01:05 PM
Post: #3




RE: 2023 in Base 37  
01062023, 06:34 PM
Post: #4




RE: 2023 in Base 37
(01062023 12:58 PM)pier4r Wrote: Nice bit of trivia! Actually base 36 is sufficient to encode the digits 0..9 and the letters A..Z, base 37 just happened to work for Joe's amusing example. Web sites often use base 64 to encode data in URL's in the form of alphanumeric strings. 

01062023, 07:58 PM
(This post was last modified: 01062023 07:59 PM by pier4r.)
Post: #5




RE: 2023 in Base 37
True! As usual I left my brain off instead of thinking for a moment that 10+26 would cover all the needed letters.
Wikis are great, Contribute :) 

01062023, 08:07 PM
(This post was last modified: 01062023 08:08 PM by toml_12953.)
Post: #6




RE: 2023 in Base 37
(01062023 01:05 PM)Maximilian Hohmann Wrote: Hello! But even a real horse has up to about 1415 HP, so we owners are allowed to have more! How much horsepower does a horse have? Tom L Cui bono? 

01062023, 08:25 PM
Post: #7




RE: 2023 in Base 37
Just for fun, here are two programs for converting integers to and from strings representing the integers in any base up to base 62. The programs are for the HP49/50 with the ListExt Library.
In the strings: The numbers 0..9 map to themselves The numbers 10..35 map to A..Z The numbers 36..61 map to a..z The first program I→STR take an integer n on level 2 and an integer b on level 1 and returns a string representing n in base b. Code:
The next program STR→I does the inverse, taking a string on level 2 and b on level 1. Code:
For example, the input 257175174 62 I→STR returns "HP50g" 

01072023, 04:06 AM
Post: #8




RE: 2023 in Base 37
This programme
https://www.hpmuseum.org/forum/thread40...light=XdYB for input 2023 2 37 returns :37: { 27 12 "." "°" 18 } 

01072023, 06:23 AM
(This post was last modified: 01072023 06:24 AM by brouhaha.)
Post: #9




RE: 2023 in Base 37
(01062023 12:21 PM)Joe Horn Wrote: New Year's trivia: 2023 in base 10 equals 1HP in base 37. Posted in the "Not Remotely" forum because no member here has only 1HP. Someone recently pointed out to me that 2023 isn't prime. I already knew that, but I had hoped that it would be choice, or at least select. Looking forward to 2027 and 2029. 

01072023, 11:17 AM
(This post was last modified: 01072023 11:35 AM by C.Ret.)
Post: #10




RE: 2023 in Base 37 for the 28's users
Hello every one,
(01062023 08:25 PM)John Keith Wrote: In the strings: Thanks for the clarification, I was wondering what to put in the conversion table after the 36th symbol, aka the Big Z character. For the one who only have \(102474081_{37}\) (and only one): First store the character conversion table as a string into the 'CC' variable: "0123456789ABCDEFGHIJKLMNOPQRSTUVWXYZabcdefghijklmnopqrstuvwxyz" 'CC' STO Note how easy is this entry to keyin since all these characters are ordered on the two keyboards and didn't need any shiftkey, except for one press on the lc key to switch into lowercase entry mode. Second enter one or both of the conversion code depending in which direction you need to convert. Both code take two arguments from the stack and return one result « → b « "" OVER LOG b LOG / FLOOR 0 FOR k SWAP b k ^ MOD LAST / IP ROT CC ROT 1 + DUP SUB + 1 STEP SWAP DROP » » ‘→BSTR’ STO n b →BSTR convert decimalbased integer n into bbase string Str. For example, 2023 37 →BSTR display "1HP" « → s b « 0 1 s SIZE FOR k b * CC s k k SUB POS 1  IF DUP 0 < OVER b ≥ OR THEN "’" s k k SUB + "’ Bad Char" + KILL ELSE + END NEXT » » ‘BSTR→’ STO Str b BSTR→ convert bbased character string Str into real integer n (or display error message when an illegal character is found anywhere in the string Str). For example, "HP50g" 62 BSTR→ return 257175174. Have had a lot of fun thanks ! Since it is the season, I wish you all \(77490_{50}\) \(81179749_{51}\) \( 80140568_{52}\) \(2G7_{28}\) ! 

01072023, 11:39 AM
Post: #11




RE: 2023 in Base 37
(01072023 11:17 AM)C.Ret Wrote: Since it is the season, I wish you all \(77490_{50}\) \(81179749_{51}\) \( 80140568_{52}\) \(2G7_{28}\) ! Yes that is a better variant of what I had in mind, finding the equivalent value for words. Also this reminds me that mathjax is active here, I totally forgot. Wikis are great, Contribute :) 

01072023, 09:59 PM
(This post was last modified: 01082023 01:34 AM by mfleming.)
Post: #12




RE: 2023 in Base 37
Another approach, using Albert's base conversion function and indexing, we could have
Code:
Extending the range of digits and encapsulating the operation as a function gives Code:
Now just need the reverse conversion to see a season's greeting! ~Mark [edit] Oops! Function base corrected per Albert [/edit] Remember kids, "In a democracy, you get the government you deserve." 

01202023, 07:41 PM
Post: #13




RE: 2023 in Base 37
Inspired by a new sequence A359840 I noticed that while 2023 is not prime in base 10, it is prime in many (perhaps infinitely many?) other bases. A quick check counted 819 bases < 10,000 in which 2023 is prime.


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