OFFSET
1,1
COMMENTS
Starting with C(1)={0,1}, C(n)={x+y| x, y in C(n-1)} union {x*y, x,y in C(n-1)}. Then a(n) is the least integer not in C(n).
LINKS
Mathematics Stack Exchange, Growth rate of the nth natural number not constructable with n steps of addition and multiplication, December 2017.
EXAMPLE
For example, C(1)={0,1}, C(2)={0,1,2}, C(3)={0,1,2,3,4}, C(4)={0,1,2,3,4,5,6,7,8,9,12,16}.
So a(1)=2, a(2)=3, a(3)=5, and a(4)=10.
PROG
(Python)
from itertools import filterfalse, count, combinations_with_replacement as cwr
n = 6
x = set([0, 1])
for i in range(n):
x = set([a[0] + a[1] for a in cwr(x, 2)]).union(set([a[0]*a[1] for a in cwr(x, 2)]))
print(next(filterfalse(lambda b: b in x, count())))
CROSSREFS
KEYWORD
nonn,more
AUTHOR
Laurence P. Bordowitz, Dec 13 2017
EXTENSIONS
a(8) from Rémy Sigrist, Dec 19 2017
STATUS
approved