A100961 - OEIS

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.

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: A067394 A337301 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