

A210614


Numbers without digit 0 or 5 whose "waterfall sequence" ends in 0,0,0,...


3



69, 78, 87, 96, 98, 169, 178, 187, 196, 619, 696, 718, 787, 817, 872, 873, 878, 916, 961, 962, 969, 1169, 1178, 1691, 1781, 2987, 6911, 6916, 6961, 6962, 6969, 7817, 7872, 7873, 7878, 8117, 8787, 9116, 9696, 9878
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OFFSET

1,1


COMMENTS

The "waterfall" sequence S for a given starting value S(1) is defined as S(n)=d(n1)*d(n) (n>1), where d(n) is the nth 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

Table of n, a(n) for n=1..40.
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

(PARI) is_A210614(n)={!setintersect(["0", "5"], Set(Vec(Str(n)))) & is_A210652(n)}
for(n=10, 9999, is_A210614(n) & print1(n", "))


CROSSREFS

Sequence in context: A168477 A264045 A295806 * A235226 A015980 A065209
Adjacent sequences: A210611 A210612 A210613 * A210615 A210616 A210617


KEYWORD

nonn,base


AUTHOR

M. F. Hasler, Mar 27 2012


STATUS

approved



