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

Larson 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. I haven't seen the Mathematics Student reference cited in Larson.

References

Author?, The Mathematics Student, 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

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

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

Crossrefs

Sequence in context: A218792 A065254 A010592 * A346252 A346253 A351953

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