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A096381 Beginning with 2, 7, multiply successive pairs of members and adjoin the result as the next one or two members of the sequence, depending on whether the product is a one- or two-digit number.

%I A096381 #30 Aug 18 2025 11:44:20
%S A096381 2,7,1,4,7,4,2,8,2,8,8,1,6,1,6,1,6,6,4,8,6,6,6,6,6,3,6,2,4,3,2,4,8,3,
%T A096381 6,3,6,3,6,3,6,1,8,1,8,1,2,8,1,2,6,8,3,2,2,4,1,8,1,8,1,8,1,8,1,8,1,8,
%U A096381 1,8,6,8,8,8,8,2,1,6,8,2,1,2,4,8,2,4,6,4,8,4,8,8,8,8,8,8,8,8,8,8,8,8,8,4,8
%N A096381 Beginning with 2, 7, multiply successive pairs of members and adjoin the result as the next one or two members of the sequence, depending on whether the product is a one- or two-digit number.
%C A096381 Berzsenyi sets the puzzle of showing that 6 occurs infinitely often in the sequence. It is easy to compose variations on the sequence, e.g., vary a(1) and a(2), or use a base other than 10, or use the product of three successive members instead of 2.
%D A096381 George Berzsenyi, Competition Corner problem 468, The Mathematics Student (published by NCTM), Vol. 26, No. 2, November 1978.
%D A096381 Loren C. Larson, Problem-Solving Through Problems, Springer, 1983, page 8, Problem 1.1.6.
%H A096381 Robert Israel, <a href="/A096381/b096381.txt">Table of n, a(n) for n = 1..10000</a>
%H A096381 George Berzsenyi, István Laukó, and Gabriella Pintér, <a href="https://www.ms-competitioncorner.com">The Competition Corner in the Mathematics Student</a>, 2021. See p. 2, problem 1/2/1.
%e A096381 a(1)a(2) = 14, so a(3) = 1 and a(4) = 4.
%p A096381 R:= 2,7: count:= 2:
%p A096381 for i from 1 while count < 200 do
%p A096381   t:= R[i]*R[i+1];
%p A096381   if t >= 10 then R:= R, floor(t/10),t mod 10; count:= count+2 else R:= R, t;
%p A096381 count:= count+1 fi;
%p A096381 od:
%p A096381 R; # _Robert Israel_, Jan 16 2018
%t A096381 Fold[Join[#, IntegerDigits[Times @@ #[[#2;;#2+1]]]] &, {2, 7}, Range[100]] (* _Paolo Xausa_, Aug 17 2025 *)
%o A096381 (Haskell) a=2:7:concat[(if x*y>9then[x*y`div`10]else[])++[x*y`mod`10]|(x,y)<-a`zip`tail a] -- Paul Stoeber (pstoeber(AT)uni-potsdam.de), Oct 08 2005
%o A096381 (Python)
%o A096381 from itertools import islice
%o A096381 from collections import deque
%o A096381 def agen(): # generator of terms
%o A096381     a = deque([2, 7])
%o A096381     while True:
%o A096381         a.extend(list(map(int, str(a[0]*a[1]))))
%o A096381         yield a.popleft()
%o A096381 print(list(islice(agen(), 105))) # _Michael S. Branicky_, Aug 18 2025
%Y A096381 Cf. A045777, A060310, A093094, A093095, A093096, A093097.
%K A096381 base,easy,nonn
%O A096381 1,1
%A A096381 _Gerry Myerson_, Aug 04 2004
%E A096381 Corrected by _Robert Israel_, Jan 16 2018