A357891 - OEIS

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

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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