%I #22 May 12 2019 16:32:34
%S 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,
%T 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,
%U 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
%N Number of applications of DENEAT operator x -> A073053(x) needed to transform n to 123.
%C 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)
%C Since each string has only finitely many preimages under this map, the sequence is unbounded. Compare A100961. - _N. J. A. Sloane_, Jun 18 2005
%D M. Ecker, Caution: Black Holes at Work, New Scientist (Dec. 1992)
%D M. J. Halm, Blackholing, Mpossibilities 69, (1999), p. 2.
%t 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 *)
%Y Cf. A073053, A100961.
%K easy,nonn,base
%O 0,1
%A _Michael Joseph Halm_, Aug 16 2002
%E Edited and corrected by _Jason Earls_ and _Robert G. Wilson v_, Jun 03 2005
%E Offset corrected by _N. J. A. Sloane_, May 12 2019