Exact Grundy Sequences for Three-Move Subtraction Games {2,b,2b-6} with Odd b

For odd b ≥ 7, we determine the complete Sprague–Grundy sequence of the subtraction game S = {2,b,2b−6}. Writing p = b−2 and L = 2p−2, the sequence agrees with the classical two-move game {2,p+2} for 0 ≤ n < L. We determine the finite transition created when the move L becomes legal and prove that, from the exact least preperiod N,g_{2,p+2,2p−2}(n) = g_{2,p−2}(n−4) (n ≥ N).This yields explicit prefix-periodic words, least eventual period p, and least preperiod N = 2p+2 for p ≡ 1 (mod 4) and N = 2p+1 for p ≡ 3 (mod 4). Ward's Case-II divisibility prediction follows as a corollary. Supplementary Material S1 provides the Lean 4 formal verification of the complete explicit Grundy sequence and the least eventual period and preperiod. Supplementary Material S2 provides the symbolic finite activation and seam audit. An independent Lean verification kit is also included.