login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo

Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 56th year, we are closing in on 350,000 sequences, and we’ve crossed 9,700 citations (which often say “discovered thanks to the OEIS”).

Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A210652 Numbers whose waterfall sequence ends in 0,0,0,.... 1
10, 15, 20, 25, 30, 35, 40, 45, 50, 51, 52, 53, 54, 55, 56, 57, 58, 60, 65, 69, 70, 75, 78, 80, 85, 87, 90, 95, 96, 98, 100, 101, 102, 103, 104, 105, 106, 107, 108, 109, 110, 115, 120, 125, 130, 135, 140, 145, 150, 151, 152, 153, 154, 155, 156, 157, 158, 159, 160, 165, 169, 170, 175, 178, 180, 185, 187, 190, 196, 200, 201, 202, 203 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

The "waterfall" sequence S for a given starting value S(1) > 9 is defined as S(n) = d(n)*d(n-1) (n > 1), where d(n) is the n-th digit of the sequence.

When S(1) has a digit 0 or 5, then S is likely to end up in repeating zeros. A210653 lists counterexamples, and A210614 is the subsequence of terms having no digit 0 or 5.

LINKS

Table of n, a(n) for n=1..73.

E. Angelini, Waterfalls (of multiplications), Mar 27 2012

E. Angelini, Waterfalls (of multiplications) [Cached copy, with permission]

PROG

(PARI) is_A210652(n, L=2e3)={ my(S=eval(Vec(Str(n)))); for(i=1, L, (S=concat(vecextract(S, "^1"), eval(Vec(Str(n=S[1]*S[2]))))) | return(1))} \\ The optional 2nd parameter L is the limit prior to which the remaining digits must be all zero. The result may be wrong if L is not large enough, but large values of L yield slow computations for values NOT in this sequence.

for(n=10, 999, is_A210652(n) & print1(n", "))

CROSSREFS

Cf. A210653.

Sequence in context: A232501 A138593 A004259 * A284804 A006623 A035166

Adjacent sequences:  A210649 A210650 A210651 * A210653 A210654 A210655

KEYWORD

nonn,base

AUTHOR

M. F. Hasler, Mar 27 2012

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified December 1 01:37 EST 2021. Contains 349426 sequences. (Running on oeis4.)