

A066409


Least positive integer not representable using exactly n 9's and the operations +*/().


0



1, 2, 1, 4, 13, 22, 33, 103, 195, 381, 934, 1858, 3747, 9166, 31279
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OFFSET

1,2


COMMENTS

This sequence allows fractions as intermediate results; else, a(9) would equal 138.  Michael S. Branicky, Feb 08 2023


LINKS



EXAMPLE

a(4)=4 because 4 cannot be expressed with exactly 4 nines and the operations +*/(). E.g. 1 = 9/9+99, 2 = 9/9+9/9, 3 = (9+9+9)/9, but 4 has no such representation.
138 = (((9  (9 / ((9 + 9) + 9))) * (9 + 9))  9)  9.
265 = ((((9  (9 / (9 + 9))) + 9) + 9) * ((9 * 9) + 9)) / 9.


PROG

(Python)
from fractions import Fraction
from functools import lru_cache
def a(n):
@lru_cache()
def f(m):
if m == 1: return {9}
out = set()
for j in range(1, m//2+1):
for x in f(j):
for y in f(mj):
out.update([x + y, x  y, y  x, x * y])
if y: out.add(Fraction(x, y))
if x: out.add(Fraction(y, x))
return out
k, s = 1, f(n)
while k in s: k += 1
return k


CROSSREFS



KEYWORD

more,nonn


AUTHOR

Joe K. Crump (joecr(AT)carolina.rr.com), Dec 24 2001


EXTENSIONS

Corrected by Leonhard Vogt (leonhard.vogt(AT)gmx.ch), Jan 09 2006


STATUS

approved



