# Python program for OEIS A061310 # Michael S. Branicky, Feb 08 2023 # A061310 Numbers which cannot be reached in the Countdown Numbers Game starting from (1,2,3,4,5,6): the game allows brackets and the operations + - x and / and not all numbers need be used, while the result of each partial calculation must be an integer. 0 data = [284, 307, 309, 314, 317, 379, 394, 398, 403, 411, 417, 423, 429, 431, 433, 435, 436, 437, 439, 441, 442, 443, 445, 446, 447, 449, 451, 453, 454, 457, 458, 459, 461, 463, 464, 466, 467, 469, 471, 473, 474, 487, 489, 491, 493, 494, 496, 499, 502, 506, 509] # (Python) from collections import Counter def canmake(v): n, vc = len(v), Counter(v) R = dict() # index of each reachable subset is [card(s)-1][s] for i in range(n): R[i] = dict() for i in range(n): R[0][(v[i], )] = {v[i]} reach = set(v) for j in range(1, n): for i in range((j+1)//2): for s1 in R[i]: for s2 in R[j-1-i]: s12c = Counter(s1 + s2) if all(s12c[e] <= vc[e] for e in s12c): s12 = tuple(sorted(s1 + s2)) if s12 not in R[len(s12)-1]: R[len(s12)-1][s12] = set() for a in R[i][s1]: for b in R[j-1-i][s2]: allowed = [a+b, a*b, a-b, b-a] if a!=0 and b%a==0: allowed.append(b//a) if b!=0 and a%b==0: allowed.append(a//b) R[len(s12)-1][s12].update(allowed) reach.update(allowed) return reach R = canmake((1,2,3,4,5,6)) # reachable set assert max(R) == 1080 ans = sorted(set(range(1081)) - R) print(ans) assert ans[:len(data)] == data with open('b061310.txt', 'w') as bfile: for n, an in enumerate(ans, 1): bfile.write(f"{n} {an}\n")