A210614 Numbers without digit 0 or 5 whose "waterfall sequence" ends in 0,0,0,...

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

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

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