T 6 N, R 5 E, Fifth Principal Meridian | Double Corners
3 mile method subdivision?? What do the field notes show?
Looks a lot like some of the overgrown sections ( 1-6) in Missouri trying to stretch to finally reach a standard parallel.
This township is in Arkansas and the GLO Records web site lists five "Original Survey" plats. The township was originally subdivided in 1824 and both the plat (two identical copies are on the BLM web site) and field notes are online.
There are several "corrections" to acreages on the township plat and those corrections appear to be the reason for all of Sec. 4 being lotted on the 1847 "Original Survey" township subdivision plat. The northern tier of sections are elongated and the 1824 plat shows the southern "half" of Sec. 4 to be regular. However, the acreage of the SE1/4 and SW 1/4 were both corrected to be 165.40 acres instead of 160 acres. In addition, Secs. 9, 16, 21, 28, 29, 32 and 33 were all reported as regular sections but show corrected acreages.
The 1847 "Original Survey" township plat (the GLO Records web site has three copies of this plat, but all are the same) shows all of those sections were lotted, most likely because of the corrected acreages shown on the 1824 township plat exceeded limits. The southern half of Sec. 33 shows the corrected acreage of the SE1/4 and SW1/4 to both be 161.34 acres. These corrected acreages appear to be within the limits at the time of the 1847 survey so they were not lotted.
Unfortunately, the 1847 field notes are not online yet. There are some other interesting things going on in this township. There is a red ink outline with comments of "Cancelled" and "Adopted Line" with a bunch of pencil and red ink "X"s.
I did find one "interesting" tidbit about the 1824 township subdivision survey. It didn't follow the township subdivision protocol that I'm familiar with. That doesn't mean anything other than I've never worked in an area where the original survey was done in 1824 so this may be a normal way of doing things at that time.
I have had more than one verification survey not show up in on-line records. Both had that look, though not identicle. It's worth contacting the BLM and asking them to run it down for you. Not sure who handles your area, but even the wrong office would be a good start.