This reverse reflects the sum of 90ⁿ
1 + 90 + 8100 + 729000 + … = ….737191

…12247191 = 13000000−800000+50000−3000+200−10+1 =

The product of 1/89 x 1/109 = 1/9701 has a beautifull equilateral symmetry.
For instance:
3311/9701=0,34130502010102051334

Likewise 1/19 is the sum of the exponential doubling sequence (2^n), with each term shifted one position to the left.
1
2
4
8
16
32
….. etc
….. 052631578947368421

Do you know if a similar sums exist for 1/13?

The emphasis here is on a long’s string’s ends, but there is one comparable consideration: the strings exact centre.

in 1/89’s case, 89 is found in the exact centre.

That would be remarkable enough..

but the same is true of 1/89’s half-brother, 1/1.09.

(correction: 10/9701= 0,0010308215….)

This is always trivially true. Any time you subtract the nearest fibonacci number, you get a smaller number (In amplitude). So you must get down to d0wn to 0. To get 0, you must subtract a number from itself. So the previous step was a fibonacci number.