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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. 1
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 (list; graph; refs; listen; history; text; internal format)
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 * A215941 A156194 A271855

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

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Last modified January 23 07:07 EST 2020. Contains 331168 sequences. (Running on oeis4.)