What is the following number called and what are its known properties? $$.12233344445555566666677777778888888899999999910101010101010101010...$$ (I think you get the pattern.)
P.S.Also, see what I did with the integer part there? :)
Asked
Active
Viewed 684 times
3
-
2I honestly don't think it has a name... – Rivasa Jul 13 '14 at 17:38
-
4It's just one of the infinitely many irrational numbers. – mfl Jul 13 '14 at 17:43
-
@mfl so is $\phi$, but it's still got a name :) – user132181 Jul 13 '14 at 17:45
-
1Yes, but $\phi,\pi,e, \cdots$ have a lot of importance in mathematics. I don't think so of the number you have written. – mfl Jul 13 '14 at 17:48
-
3OK, so let's give it a name: "user132181's number". – Robert Israel Jul 13 '14 at 17:49
-
1@RobertIsrael my life is complete now! :) – user132181 Jul 13 '14 at 17:50
-
1It is not direct, but if you replace each repeated digit by $0001$ of appropriate length, you have http://en.wikipedia.org/wiki/Ramanujan_theta_function Ramanujan's $f(1/10,1).$ I suspect this is included in hte proofs of transcendency by Wadim Zudilin's adviser, Nesterenko http://genealogy.math.ndsu.nodak.edu/id.php?id=83363 I imagine standard manipulations with power series, such as are often asked about on MSE, should take this to your number. My guess is transcendental. Here we go, identity for $f(q,q^3)$ is better. – Will Jagy Jul 13 '14 at 17:56
-
1See Champernowne constant, Copeland-Erdos constant, and Liouville number. – Lucian Jul 13 '14 at 18:04
-
@Lucian I do know about these as well, and they too look an awful lot similiar to the number above, but still... who knows? Maybe this number has some magical super-properties that none of the other popular numbers has. – user132181 Jul 13 '14 at 18:10
-
I read it as $10$ repeating so, I thought, it's a rational. But, now, I see it... – James S. Cook Jul 13 '14 at 19:18
-
As an integer sequence it has an entry in the OEIS. – Antoni Parellada Nov 30 '20 at 19:42
1 Answers
-3
It shares thematic similarity w/ the "look and say sequence" described by John Horton Conway in the mid 1980s. That's a pyramid where every row beneath the first one 'describes' the previous row (e.g. The second row '1 1' describes the first row '1' when spoken as "one one").
ursus_m
- 3
-
1Yes, I know about that sequence and it does feel a bit similar to the number above, but unfortunately this doesn't answer my question :( – user132181 Jul 13 '14 at 18:05