%I #19 Feb 15 2024 14:20:06
%S 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,
%T 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,
%U 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
%N a(1)=1, a(2)=2; thereafter successive products of pairs of digits make further digits.
%C The numbers 0, 5, 7, and 9 never appear, but arbitrarily long sequences of 8's appear.
%H T. D. Noe, <a href="/A045777/b045777.txt">Table of n, a(n) for n = 1..15212</a>
%H Erich Friedman, <a href="https://erich-friedman.github.io/puzzle/mathpuzzle/">Puzzles of the Week</a>.
%e 1*2=2 2*2=4 2*4=8 4*8=32 8*3=24...
%t t = {1, 2}; Do[ t = Join[t, IntegerDigits[t[[n-1]] t[[n-2]]]], {n, 3, 100}]; t
%o (Python)
%o from itertools import islice
%o from collections import deque
%o def agen(): # generator of terms
%o a = deque([1, 2])
%o while True:
%o a.extend(list(map(int, str(a[0]*a[1]))))
%o yield a.popleft()
%o print(list(islice(agen(), 105))) # _Michael S. Branicky_, Feb 15 2024
%K easy,nonn,base
%O 1,2
%A _Erich Friedman_