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

0,1

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.

Links

Table of n, a(n) for n=0..99.

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 *)

Crossrefs

Cf. A073053, A100961.

Sequence in context: A220319 A220342 A221676 * A010695 A021400 A059855

Adjacent sequences: A073051 A073052 A073053 * A073055 A073056 A073057

Keyword

easy,nonn,base

Author

Michael Joseph Halm, Aug 16 2002

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

Status

approved