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

Author

Amarnath Murthy and Paul D. Hanna, Sep 11 2003

Keywords

• nonn
• base

Examples

			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.
		

Links

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

Crossrefs

Cf. A087471, A087472, A087474.

Programs

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 *)

Extensions

More terms from Ray Chandler, Sep 19 2003

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