If you want to create the above irrational to any degree of accuracy just start your algorithm with a odd integer like 99 and find its' reciprocal (1/99) then add 97 and find that reciprocal and so on until you add the final odd(5) which will give you the above irrational -- 5.14064682573322848552...
This can be accomplished in a split second with the right algorithm and reflect the same irrational produced by (1/(e^2 -7))*2 Because the algorithm starts with a very small odd only a certain number of digits will match the above formula which is correct --->oo.
The best way to explain this better is produce the irrational with the formula above and start by subtracting the (5) then find the reciprocal of the remainder (1/r). (7) will appear to the left of the decimal then subtract the (7) then (1/r) and so on. You will end up at each point subtracting these integers-- 5,7,9,11,13,15,17,19... ---> all the odd integers -->oo
Hope this helps
I am looking at the other part of your last post and will get back to you.