x-0-112123123412345123456-decimal-pattern-1-12-123-Can-this-be-represented-as-a-fraction-or-is-this-number-trancendental-

Question Number 6449 by Temp last updated on 27/Jun/16

x = 0.112123123412345123456 \dots

decimal pattern : 1, 12, 123, \dots

Can this be represented as a fraction ?

or is this number trancendental ?

Commented by prakash jain last updated on 28/Jun/16

123456 may have some inputs on this

sequence .

Commented by prakash jain last updated on 27/Jun/16

What comes after

12345689

12345678910 ?

If the pattern is non - repeating then it

will be irrational .

It is generally very hard to prove if a

number is trancendental .

Commented by Temp last updated on 28/Jun/16

12345678910, 1234567891011, e t c .

and I see

Commented by nburiburu last updated on 28/Jun/16

t h i s n u m b e r i s g e n e r a l i z e d a s

x = \underset{n = 0}{\sum^{\infty}} (\frac{n - \frac{⌊ \frac{\sqrt{8 n + 1} - 1}{2} ⌋ (⌊ \frac{\sqrt{8 n + 1} - 1}{2} ⌋ + 1)}{2} + 1}{10^{n (n + 1) / 2}})

(S m a d a r a n c h e c r e c e n d o s e q u e n c e /

10 t o t h e s u m f r o m 1 t o n)

I t i s n o t a r a t i o n a l n u m b e r .

Commented by prakash jain last updated on 28/Jun/16

This is good information . Thanks .

I will look up derivation of the formula .