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.

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, 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, 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

Offset: 1

Author

Gerry Myerson, Aug 04 2004

Keywords

• base
• easy
• nonn

Comments

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.

Examples

			a(1)a(2) = 14, so a(3) = 1 and a(4) = 4.
		

References

• George Berzsenyi, Competition Corner problem 468, The Mathematics Student (published by NCTM), Vol. 26, No. 2, November 1978.
• Loren C. Larson, Problem-Solving Through Problems, Springer, 1983, page 8, Problem 1.1.6.

Links

• Robert Israel, Table of n, a(n) for n = 1..10000
• George Berzsenyi, István Laukó, and Gabriella Pintér, The Competition Corner in the Mathematics Student, 2021. See p. 2, problem 1/2/1.

Crossrefs

Cf. A045777, A060310, A093094, A093095, A093096, A093097.

Programs

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

Maple

R:= 2,7: count:= 2:
for i from 1 while count < 200 do
  t:= R[i]*R[i+1];
  if t >= 10 then R:= R, floor(t/10),t mod 10; count:= count+2 else R:= R, t;
count:= count+1 fi;
od:
R; # Robert Israel, Jan 16 2018

Mathematica

Fold[Join[#, IntegerDigits[Times @@ #[[#2;;#2+1]]]] &, {2, 7}, Range[100]] (* Paolo Xausa, Aug 17 2025 *)

Python

from itertools import islice
from collections import deque
def agen(): # generator of terms
    a = deque([2, 7])
    while True:
        a.extend(list(map(int, str(a[0]*a[1]))))
        yield a.popleft()
print(list(islice(agen(), 105))) # Michael S. Branicky, Aug 18 2025

Extensions

Corrected by Robert Israel, Jan 16 2018