I was bored and typed sqrt(546) into wolfram and made it show as many digits as it was capable of...
Why would you even think to search it though, if you didn't already know it was related to ponies?
idk i just fucking searched it dude
Just tested it with the first 99960 digits of sqrt(546)
10026 dubs
1010 trips
97 quads
which are all in good agreement with the theoretical expectation (9996, 1000, 100).
>1000, 100
999.6, 99.96 surely?
>hell even some quads
Given any sequence of 4 digits, the odds that the 2nd, 3rd, and 4th are the same as the 1st is 1/10 x 1/10 x 1/10 = 1/1000. So every thousandth set of 4 digits will be a quad, on average.
You have, what, 2500 digits there? Somewhere close to that. So there should be 2 or 3 quads there, along with about 25 trips and 250 dubs.
Oh, but then there's the fact that every individual digit could be the start of a 4 digit sequence, so there'll be more quads than that.
question:
are there ALGEBRAIC nubers i.e. irrational numbers formed by square routes of rational numbers which have properties like
e.g." no digit in base 10 of a^(1/b) is the digit 2 where a and b are both rational"
or similar properties that only make sense in base 10?
how would you go about proving hat there is no such algebraic number with those kinds of properties?
that for every pattern specific to base 10 you specify, like "this algebraic number only has the digit "2" when the power of 10 column is a multiple of 5" every algebraic number will eventually violate that pattern after enough digits
Actually 4569 digits after the decimal.
6 quads total.
Well at least I can find one counterexample with a = 1 and b = 1, since 1 has no digit 2
For your second example you can have the number 0.000020000200002... which would be rational, and thus algebraic.