help needed for correspondent of Oct 9

[T. D. Noe]

>Dear Seqfans,  Could someone help this person?  And post the
>result to the list.  Thanks!  Neil
>
>>From ghughes at cei.net  Sun Oct  9 16:38:24 2005
>From: "Grover Hughes" <ghughes at cei.net>
>To: <njas at research.att.com>
>Subject: new (?) sequence
>Date: Sun, 9 Oct 2005 15:38:19 -0500
>Dear Mr. Sloane:
>
>I was playing around with continued factions and came across the =
>following:
>
>x =3D 1 + 2/(3 + 4/(5 + 6/7 + 8/ ....
>
>which seems to converge on the value=20
>
>   1.54149408....
>
>after some 17 terms of the continued fraction are used. Does this number =
>mean anything to you? I'm curious to know, not that it has any practical =
>value, but just for personal satisfaction.


According to Plouffe's Inverter, the number appears to be
(e^(1/2)+1)/(e-1), which is the same as 1/(e^(1/2)-1).

Tony