A357891 a(1) = 1; a(n+1) is the smallest integer > 0 that cannot be obtained from the integers {a(1), ..., a(n)} using each number exactly once and the operators +, -, *, /.

1, 2, 4, 11, 34, 152, 1079, 6610, 93221

Offset

1,2

Links

Table of n, a(n) for n=1..9.

Prog

(Python)
from fractions import Fraction
def a(n, 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]:
                    if set(s1) & set(s2) == set():
                        s12 = tuple(sorted(set(s1) | set(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: allowed.append(Fraction(b, a))
                                if b!=0: allowed.append(Fraction(a, b))
                                R[len(s12)-1][s12].update(allowed)
    k = 1
    while k in R[n-1][tuple(v)]: k += 1
    return k
alst = [1]
[alst.append(a(n, alst)) for n in range(1, 6)]
print(alst) # Michael S. Branicky, Nov 01 2022

Crossrefs

Cf. A071115, A217043, A358075.

Sequence in context: A238425 A358075 A071115 * A217043 A249696 A156809

Adjacent sequences: A357888 A357889 A357890 * A357892 A357893 A357894

Keyword

nonn,hard,more

Author

Rainer Rosenthal and Hugo Pfoertner, Nov 01 2022

Extensions

a(9) from Michael S. Branicky, Nov 10 2022

Status

approved