A087473 Smallest positive number that requires n iterations of f(k) to reach a single digit, where f(k) is the product of the two numbers formed from the alternating digits of k.

1, 10, 25, 39, 77, 171, 199, 577, 887, 1592, 2682, 3988, 6913, 18747, 39577, 58439, 99428, 173442, 267343, 299137, 574182, 685812, 880543, 1635812, 1974447, 2771717, 18871813, 45797337, 49899368, 58935768, 158504329, 265956179, 566800111, 896125563

Offset

0,2

Links

Giovanni Resta, Table of n, a(n) for n = 0..40

Example

a(4)= 77 since 77 is the smallest number that requires 4 iterations to reach a single digit: f(77)=7*7=49, f(49)=4*9=36, f(36)=3*6=18, f(18)=1*8=8.

Mathematica

f[n_] := Block[{d = IntegerDigits@ n}, If[OddQ@ Length@ d, PrependTo[d, 0]]; Times @@ FromDigits /@ Transpose@ Partition[d, 2]]; a[n_] := Block[ {c=-1, m}, t=0; While[c != n, t++; m=t; c=0; While[m > 9, c++; m = f@ m]]; t]; a /@ Range[0, 12] (* Giovanni Resta, Aug 01 2018 *)

Crossrefs

Cf. A087471, A087472, A087474.

Sequence in context: A154057 A074814 A002600 * A014120 A003001 A198377

Adjacent sequences: A087470 A087471 A087472 * A087474 A087475 A087476

Keyword

nonn,base

Author

Amarnath Murthy and Paul D. Hanna, Sep 11 2003

Extensions

More terms from Ray Chandler, Sep 19 2003

a(30)-a(33) from Giovanni Resta, Aug 01 2018

Status

approved