OFFSET
1,1
COMMENTS
The "waterfall" sequence S for a given starting value S(1) is defined as S(n)=d(n-1)*d(n) (n>1), where d(n) is the n-th digit of the sequence.
When a(0) has a digit 0 or 5, then S is likely to end up in repeating zeros, which is the motivation for the definition of this sequence.
LINKS
E. Angelini, Waterfalls (of multiplications), Mar 27 2012
E. Angelini, Waterfalls (of multiplications) [Cached copy, with permission]
EXAMPLE
The waterfall sequence for S(1)=69 is S=(69,54,45,20,16,20,10,0,0,6,12, 0,0,0,0,0,0,6,2,0,0,0,0,0,0,0,12,0,0,0,0,0,0,0,0,2,0,0,0,...) with S(2)=6*9=54, S(3)=9*5=45, S(4)=5*4=20, etc.
The last "2" is obtained as 1*2 from the digits of term S(27)=12, thereafter there are no two consecutive nonzero digits and therefore only 0's can follow.
Similarly, for S(1)=78, one has S=(78,56,40,30,24,0,0,0,0,8,0,0,0,...), and only zeros thereafter since d(10)=4 is the last nonzero digit having a nonzero neighboring digit (d(9)=2, which yields S(10)=2*4=8).
PROG
CROSSREFS
KEYWORD
nonn,base
AUTHOR
M. F. Hasler, Mar 27 2012
STATUS
approved