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A093095 Start with a(1) = 2, a(2) = 3, then apply the rule of A093094.

%I A093095 #18 Aug 18 2025 12:02:18
%S A093095 2,3,6,1,8,6,8,4,8,4,8,3,2,3,2,3,2,3,2,2,4,6,6,6,6,6,6,6,4,8,2,4,3,6,
%T A093095 3,6,3,6,3,6,3,6,3,6,2,4,3,2,1,6,8,1,2,1,8,1,8,1,8,1,8,1,8,1,8,1,8,1,
%U A093095 8,1,8,1,8,1,8,1,2,8,1,2,6,2,6,4,8,8,2,2,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8
%N A093095 Start with a(1) = 2, a(2) = 3, then apply the rule of A093094.
%D A093095 Hugo Steinhaus, Studentenfutter, Urania, Leipzig 1991, #1.
%H A093095 Reinhard Zumkeller, <a href="/A093095/b093095.txt">Table of n, a(n) for n = 1..10000</a>
%e A093095 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)=a(3)*a(4)
%t A093095 Fold[Join[#, IntegerDigits[Times @@ #[[#2;; #2+1]]]] &, {2, 3}, Range[100]] (* _Paolo Xausa_, Aug 18 2025 *)
%o A093095 (Haskell)
%o A093095 a093095 n = a093095_list !! (n-1)
%o A093095 a093095_list = f [2,3] where
%o A093095    f (u : vs@(v : _)) = u : f (vs ++
%o A093095      if w < 10 then [w] else uncurry ((. return) . (:)) $ divMod w 10)
%o A093095         where w = u * v
%o A093095 -- _Reinhard Zumkeller_, Aug 08 2013
%o A093095 (Python)
%o A093095 from itertools import islice
%o A093095 from collections import deque
%o A093095 def agen(): # generator of terms
%o A093095     a = deque([2, 3])
%o A093095     while True:
%o A093095         a.extend(list(map(int, str(a[0]*a[1]))))
%o A093095         yield a.popleft()
%o A093095 print(list(islice(agen(), 105))) # _Michael S. Branicky_, Aug 18 2025
%Y A093095 Cf.  A045777, A060310, A093094, A093096, A093097, A096381.
%K A093095 nonn,base
%O A093095 1,1
%A A093095 _Bodo Zinser_, Mar 20 2004