Curious why the grid ascends in units of 4.
Room for expansion.
The E-W signed basic state route system seems to work like this: starting with 2 (unsigned), there's 6, then 10 farther south, unassigned 14, 18, 22, 26 & 30 held back because of US highways (although original OR 26 was US 20 from the coast to the Willamette Valley), 34, 38, 42, 46, former 50 and 54, 58, 62, 66, 70, 74, 78, 82, 86 (a later addition). All even, and
not divisible by 4. The ones that
are divisible by 4: 8, former 32, 36, 52 are all former US routes (in order 26, 30, and 28 for the last two). N-S state routes advance by increments of 4 starting with 3 (and, correctly deduced, 37 should be 15 according to the grid) with 7, 11, 19, unassigned 23, 27, 31, 35, 39, 43, 47, and 51. And again, interim odd numbers are former US highway alignments: 37 (see above) and 53. One could see this as a sort of fractured grid pattern starting in the northeast corner of the state. Curiously, OR could be said to have taken a cue from the original CA grid pattern, which laid out even-numbered highways divisible by 4 from about Stockton and basically progressing northward to the original CA 44 (with the original 28 being an outlier), while even numbers not divisible by 4 started in the northern part of the L.A. basin and originally progressed south and southeast into Orange County, ending in 26, with the extended range in the 30's located in the east and west exurbs. Because of topology, the N-S odd-numbered routes were never able to extend a workable grid pattern, so "clusters" became the stock in trade: 1, 5, 9, 13, 17, 21, 25, 29 in or extending out from the Bay Area, with 3, 7, 11, 15, 19, 23, 27, unassigned 31, 35, 39 scattered around greater L.A. IMO, it's a shame the Division of Highways didn't "double-down" on the original grid pattern in the '64 renumbering!
But of the two states, OR's system has maintained more of the original attempted grid pattern, even with US 20 and 26 subsuming much of the original long-distance state routes east of the Willamette Valley (54 & 50 respectively).