A073054 Number of applications of DENEAT operator x -> A073053(x) needed to transform n to 123.

2, 5, 2, 5, 2, 5, 2, 5, 2, 5, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 3, 2, 3, 2, 3, 2, 3, 2, 3, 2, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 3, 2, 3, 2, 3, 2, 3, 2, 3, 2, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 3, 2, 3, 2, 3, 2, 3, 2, 3, 2, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 3, 2, 3, 2, 3, 2, 3, 2, 3, 2, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4

Offset: 0

Author

Michael Joseph Halm, Aug 16 2002

Keywords

• easy
• nonn
• base

Comments

0 first occurs for n=123, 1 first occurs for n=101, 2 first occurs for n=0, 3 first occurs for n=20, 4 first occurs for n=11, 5 first occurs for n=1. What is the least n such that a(n) > 5? - Jason Earls, Jun 03 2005 (Corrected by N. J. A. Sloane, May 12 2019)

Since each string has only finitely many preimages under this map, the sequence is unbounded. Compare A100961. - N. J. A. Sloane, Jun 18 2005

References

• M. Ecker, Caution: Black Holes at Work, New Scientist (Dec. 1992)
• M. J. Halm, Blackholing, Mpossibilities 69, (1999), p. 2.

Crossrefs

Cf. A073053, A100961.

Programs

Mathematica

f[n_] := Block[{id = IntegerDigits[n]}, FromDigits[ Join[ IntegerDigits[ Length[ Select[id, EvenQ[ # ] &]]], IntegerDigits[ Length[ Select[id, OddQ[ # ] &]]], IntegerDigits[ Length[ id]] ]]]; Table[ Length[ NestWhileList[f, n, UnsameQ, All]] - 2, {n, 0, 104}] (* Robert G. Wilson v, Jun 09 2005 *)

Extensions

Edited and corrected by Jason Earls and Robert G. Wilson v, Jun 03 2005

Offset corrected by N. J. A. Sloane, May 12 2019