Proposed OEIS updates from q1

Drafts for Stephen to submit; nothing here has been sent.

A173419 (τ(n), programs from 1 with +, −, ×)

b-file extension: tau_table_10266.txt gives τ(n) for 1 ≤ n ≤ 10266, agreeing with the existing b-file for n ≤ 1800. Every n ≤ 10266 is reached within 9 steps (10267 is the least n with τ(n) = 10, A141414), so the table is exact. Computed twice (C and Rust) by exhaustive enumeration of all normalised programs of at most 9 steps.
Comment check: the four primes p < 5000 with τ(p) < τ(p−1) are 3359, 3623, 4909, 4943, as stated in the comment of 28 Aug 2026.

a(13)–a(19) replayed: complete 11-step and 12-step searches with exact arithmetic (no modular reduction, no size cap) confirm 13! and 14! at 11, 15!, 16!, 17! at 12, and no 12-step program for 18! and 19!.
a(20), a(21), a(22): pending the 13-step decision (this folder, decide13.json).

τ(29#) = 12 and τ(31#) = 12, with programs in decide12.json; the lower bound 12 is the complete 11-step search. Markström (INTEGERS 14, 2014, Figure 5) had 13 and 15.