A210652 Numbers whose waterfall sequence ends in 0,0,0,....

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

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: A138593 A362010 A004259 * A284804 A006623 A035166

Adjacent sequences: A210649 A210650 A210651 * A210653 A210654 A210655

Keyword

nonn,base

Author

M. F. Hasler, Mar 27 2012

Status

approved