### Decimal expansion = Continued fraction

Posted:

**Wed May 16, 2018 4:45 am**Someone posed this problem to me: Is there a number whose decimal expansion is equal to its continued fraction expansion? That is, if a,b,c,d,etc are digits, is there a number satisfying

a.bcde... = [a;b,c,d,e,...] ?

With some coding, I found a number that satisfies this criteria for the first four digits after the decimal point, but I haven't found a better one. Can you?

Can one also find a number that satisfies the criteria for all digits, or prove such a number cannot exist?

a.bcde... = [a;b,c,d,e,...] ?

With some coding, I found a number that satisfies this criteria for the first four digits after the decimal point, but I haven't found a better one. Can you?

Can one also find a number that satisfies the criteria for all digits, or prove such a number cannot exist?