Also,
all odd numbers mod 16 are 1 3 5 7 9 11 13 15, and squared have 1 of 2 results.
#/.~ 16 | *: 3 + 2 * i.2000
1000 1000
similarly to odd numbers mod 10 squared are 1 and 9 and 5.
Its a bit interesting that there are slightly more 9s than 1s and it increases
somewhat irregularly in each range.
#/.~ 16 | *: p: >: i.1000
506 494
#/.~ 16 | *: p: >: i.2000
1005 995
#/.~ 16 | *: p: >: i.3000
1508 1492
#/.~ 16 | *: p: >: i.4000
2018 1982
#/.~ 16 | *: p: >: i.5000
2522 2478
----- Original Message -----
From: Devon McCormick <[email protected]>
To: J-programming forum <[email protected]>
Sent: Monday, January 4, 2016 9:13 PM
Subject: [Jprogramming] Prime-based selection oddity
Recently I was looking at how I might generate something that look like an
encryption key and noticed this oddity:
#val=. '0123456789ABCDEF'
16
val{~(#val)|2^~p:i.128
49919919191919199991119119199119199199199911919199111911919199911991991119919911991119119191199191999991919111191911919991999991
frtab val{~(#val)|2^~p:i.128
+--+-+
|1 |4|
+--+-+
|68|9|
+--+-+
|59|1|
+--+-+
Where "frtab" is a frequency table generator:
frtab=: 3 : 0
cts=. #&>y</.y NB. # unique items...
if. -.isNum y do. NB. Special case enclosed, text mat, text vec,
if. (L.=0:) y do. (<"0 cts),.<"0 ~.y else.
if. 2=#$y do. (<"0 cts),.<"1 ~.y else. (<"0 cts),.<"0 ~.y end.
end.
else. cts,.~.y end. NB. and simple numeric vec.
NB.EG (1 2 3 2 1,. 11 22 33 222 99) -: frtab 11 22 22 33 33 33 222 222 99
)
Any obvious reason why the 16| of squares of primes should return only "1"
and "9" for this sample?
--
Devon McCormick, CFA
Quantitative Consultant
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