A045777 a(1)=1, a(2)=2; thereafter successive products of pairs of digits make further digits.

1, 2, 2, 4, 8, 3, 2, 2, 4, 6, 4, 8, 2, 4, 2, 4, 3, 2, 1, 6, 8, 8, 8, 1, 2, 6, 2, 6, 4, 8, 6, 4, 6, 4, 8, 2, 1, 2, 1, 2, 1, 2, 2, 4, 3, 2, 4, 8, 2, 4, 2, 4, 2, 4, 3, 2, 1, 6, 2, 2, 2, 2, 2, 2, 4, 8, 1, 2, 6, 8, 3, 2, 1, 6, 8, 8, 8, 8, 8, 1, 2, 6, 2, 6, 1, 2, 4, 4, 4, 4, 4, 8, 3, 2, 8, 2, 1, 2, 4, 8, 2, 4, 6, 2, 6

Offset: 1

Author

Erich Friedman

Keywords

• easy
• nonn
• base

Comments

The numbers 0, 5, 7, and 9 never appear, but arbitrarily long sequences of 8's appear.

Examples

			1*2=2 2*2=4 2*4=8 4*8=32 8*3=24...
		

Links

• T. D. Noe, Table of n, a(n) for n = 1..15212
• Erich Friedman, Puzzles of the Week.

Programs

Mathematica

t = {1, 2}; Do[ t = Join[t, IntegerDigits[t[[n-1]] t[[n-2]]]], {n, 3, 100}]; t

Python

from itertools import islice
from collections import deque
def agen(): # generator of terms
    a = deque([1, 2])
    while True:
        a.extend(list(map(int, str(a[0]*a[1]))))
        yield a.popleft()
print(list(islice(agen(), 105))) # Michael S. Branicky, Feb 15 2024