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

1,1

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.

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.

Example

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

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 *)

Prog

(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
(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

Crossrefs

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

Sequence in context: A218792 A065254 A010592 * A383187 A346252 A346253

Adjacent sequences: A096378 A096379 A096380 * A096382 A096383 A096384

Keyword

base,easy,nonn

Author

Gerry Myerson, Aug 04 2004

Extensions

Corrected by Robert Israel, Jan 16 2018

Status

approved