Joe;
12ga = .729"
13ga = .710"
14ga = .693"
15ga = .677"
16ga = .662"
To find dimension for 13/1 simply add the .729" & .710", Divide by 2 & drop (don't round) beyond three decimal places. thus .729+.710/2 = .7195 & drop the .0005.
You were right in theory, but somewhere picked up the 13/1 dia for 13ga.
The full gauges are worked by a mathamatical formula & all "Rounded to three decimals, but the in-between sizes are averaged & simply dropped to three places.
Beginning with 10 ga where there are two in-betweens the steps are 1/3 & 2/3 of the space between whole gas, & still dropped to three places, not rounded.

Miller/TN
I Didn't Say Everything I Said, Yogi Berra