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A093096 Start with a(1) = a(2) = 3; then apply the rule of A093094.

%I A093096 #17 Aug 18 2025 12:02:00
%S A093096 3,3,9,2,7,1,8,1,4,7,8,8,4,2,8,5,6,6,4,3,2,8,1,6,4,0,3,0,3,6,2,4,1,2,
%T A093096 6,1,6,8,6,2,4,0,0,0,0,1,8,1,2,8,4,2,1,2,6,6,4,8,4,8,1,2,8,0,0,0,0,0,
%U A093096 8,8,2,1,6,3,2,8,2,2,1,2,3,6,2,4,3,2,3,2,3,2,8,2,1,6,0,0,0,0,0,0,6,4,1,6,2
%N A093096 Start with a(1) = a(2) = 3; then apply the rule of A093094.
%C A093096 Essentially the same as A060310. [From _R. J. Mathar_, Sep 08 2008]
%D A093096 Hugo Steinhaus, Studentenfutter, Urania, Leipzig 1991, #1.
%H A093096 Reinhard Zumkeller, <a href="/A093096/b093096.txt">Table of n, a(n) for n = 1..10000</a>
%e A093096 a(3)=a(1)*a(2), a(4)=first digit of (a(2)*a(3)), a(5)=2nd digit of (a(2)*a(3)), a(6)=first digit of (a(3)*a(4)), a(7)=2nd digit of (a(3)*a(4))
%t A093096 Fold[Join[#, IntegerDigits[Times @@ #[[#2;; #2+1]]]] &, {3, 3}, Range[100]] (* _Paolo Xausa_, Aug 18 2025 *)
%o A093096 (Haskell)
%o A093096 a093096 n = a093096_list !! (n-1)
%o A093096 a093096_list = f [3,3] where
%o A093096    f (u : vs@(v : _)) = u : f (vs ++
%o A093096      if w < 10 then [w] else uncurry ((. return) . (:)) $ divMod w 10)
%o A093096         where w = u * v
%o A093096 -- _Reinhard Zumkeller_, Aug 13 2013
%o A093096 (Python)
%o A093096 from itertools import islice
%o A093096 from collections import deque
%o A093096 def agen(): # generator of terms
%o A093096     a = deque([3, 3])
%o A093096     while True:
%o A093096         a.extend(list(map(int, str(a[0]*a[1]))))
%o A093096         yield a.popleft()
%o A093096 print(list(islice(agen(), 105))) # _Michael S. Branicky_, Aug 18 2025
%Y A093096 Cf. A045777, A060310, A093094, A093095, A093097, A096381.
%K A093096 nonn,base
%O A093096 1,1
%A A093096 _Bodo Zinser_, Mar 20 2004