What is the first 12-digit sequence in the duodecimal expansion of pi that contains each digit exactly once?
I can reaffirm my assessment here. Larry was correct
in suggesting that a computation of Pi Base 12
requires a base 10 input some 8% longer (or more)
in decimal places.
Checking shorter length computations
of Pi, base 12, against a 400,000 length
computation below, we see at what decimal place the
shorter computation fails.
decimal length failure point
-------------------------------------------
size = 1,000 fails at 927
size = 2,000 fails at 1,854
size = 2,160 checks completely
size = 3,000 fails at 2,780
size = 4,000 fails at 3,707
size = 10,000 fails at 9,266
size = 20,000 fails at 18,534
size = 30,000 fails at 27,799
size = 50,000 fails at 46,331
size = 100,000 checks completely
size = 200,000 checks completely
So, when I found a "solution" - a series starting at digit
28,641 using a 30,000 digit computation, I was fooled
by the inaccuracy that started at digit 27,799.
The actual solution at digit 30,762 stands against all much
more accurate input (to 400,000 places values of Pi, where 200,009
are verified).
I also ran Larry's 1.08 x 2,000 = 2,160 case with my s/w but, for me,
this produced a correct 2,160 digit Pi base 12, supporting
the idea that since his Pi diverged at digit 271, more likely
he indeed had a bug, rather than imprecision, which
was what befell me.
Edited on November 8, 2023, 4:02 am
more accuracy checks
