A296261 Least non-constructible integer after addition or multiplication.

2, 3, 5, 10, 26, 178, 7391, 6550891

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

Table of n, a(n) for n=1..8.

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

Sequence in context: A011832 A011833 A007695 * A133662 A204518 A336991

Adjacent sequences: A296258 A296259 A296260 * A296262 A296263 A296264

Keyword

nonn,more

Author

Laurence P. Bordowitz, Dec 13 2017

Extensions

a(8) from Rémy Sigrist, Dec 19 2017

Status

approved