

A100961


For a decimal string s, let f(s) = decimal string ijk, where i = number of even digits in s, j = number of odd digits in s, k=i+j (see A171797). Start with s = decimal expansion of n; a(n) = number of applications of f needed to reach the string 123.


6



2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 3, 2, 3, 2, 3, 2, 3, 2, 3, 3, 2, 3, 2, 3, 2, 3, 2, 3, 2, 2, 3, 2, 3, 2, 3, 2, 3, 2, 3, 3, 2, 3, 2, 3, 2, 3, 2, 3, 2, 2, 3, 2, 3, 2, 3, 2, 3, 2, 3, 3, 2, 3, 2, 3, 2, 3, 2, 3, 2, 2, 3, 2, 3, 2, 3, 2, 3, 2, 3, 3, 2, 3, 2, 3, 2, 3, 2, 3, 2, 2, 3, 2, 3, 2, 3, 2, 3, 2, 3, 2, 1, 2, 1, 2
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OFFSET

0,1


COMMENTS

Obviously if the digits of m and n have the same parity then a(m) = a(n). E.g. a(334) = a(110). In other words, a(n) = a(A065031(n)).
It is easy to show that (i) the trajectory of every number under f eventually reaches 123 (if s has more than three digits then f(s) has fewer digits than s) and (ii) since each string ijk has only finitely many preimages, a(n) is unbounded.


LINKS

Reinhard Zumkeller, Table of n, a(n) for n = 0..10000


EXAMPLE

n=0: s=0 > f(s) = 101 > f(f(s)) = 123, stop, a(0) = 2.
n=1: s=1 => f(s) = 011 > f(f(s)) = 123, stop, f(1) = 2.


CROSSREFS

A073054 gives another version. f(n) is (essentially) A171797 or A073053.
Cf. A065031, A308002.
Sequence in context: A098708 A067394 A076925 * A263206 A230501 A287272
Adjacent sequences: A100958 A100959 A100960 * A100962 A100963 A100964


KEYWORD

nonn,easy,base


AUTHOR

N. J. A. Sloane, Jun 17 2005


EXTENSIONS

More terms from Zak Seidov, Jun 18 2005


STATUS

approved



