A097154 Number of iterations of f(x) = reverse(x) - maxdigit(x) needed to reach zero, or -1 if zero is never reached, where maxdig(n) is the largest digit of n.

1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 4, 4, 4, 5, 3, 3, 3, 3, 1, 2, 2, 4, 4, 6, 5, 3, 3, 3, 1, 2, 2, 2, 4, 4, 7, 3, 3, 3, 1, 2, 2, 2, 2, 4, 4, 5, 3, 3, 1, 2, 2, 2, 2, 2, 4, 6, 3, 3, 1, 2, 2, 2, 2, 2, 2, 4, 5, 3, 1, 2, 2, 2, 2, 2, 2, 2, 4, 3, 1, 2, 2, 2, 2, 2, 2, 2, 2, -1, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 6, 6, 9, 7, 8, 8, 10, 7, 2, 3, 10, 7, 8, 9, 3, 3, 3, 3, 4, 4, 4, 4, 4, 8, 4, 4

Offset

1,11

Comments

a(89)=-1 because 89 is the first number that will not reach zero: 98-9=89. It is conjectured that 0 and 89 are the only fixed points of f. See A097155 for numbers that reach 89.

Links

Table of n, a(n) for n=1..127.

Example

a(12)=4 because 12 -> 19 -> 82 -> 20 -> 0.

Crossrefs

Cf. A097153, A097155, A097156, A097157, A097158.

Sequence in context: A162798 A088650 A390942 * A108421 A104058 A132345

Adjacent sequences: A097151 A097152 A097153 * A097155 A097156 A097157

Keyword

base,easy,sign

Author

Jason Earls, Aug 01 2004

Status

approved