%I #11 Aug 05 2014 09:18:42
%S 0,0,0,1,1,2,0,1,3,1,2,0,1,2,4,0,0,1,3,4,2,1,1,2,1,0,1,3,1,2,0,1,2,4,
%T 0,0,1,3,4,2,1,1,2,1,0,0,1,3,2,4,0,0,1,3,4,2,1,1,2,1,0,0,0,0,0,0,1,3,
%U 4,2,1,1,2,1,0,0,0,0,0,0,1,3,5,7,8,1,0
%N a(n) = the difference between the n-th node of the infinite trunk of the factorial beanstalk (A219666(n)) and the smallest integer (A219653(n)) which is as many A219651-iteration steps distanced from the root (zero); a(n) = A219666(n) - A219653(n).
%C For all n, the following holds: A219653(n) <= A219666(n) <= A219655(n). This sequence gives the distance of the node n in the infinite trunk of factorial beanstalk (A219666(n)) from the left (lesser) edge of the A219654(n) wide window which it at that point must pass through.
%C This sequence relates to the factorial base representation (A007623) in the same way as A218603 relates to the binary system and similar remarks apply here.
%H Antti Karttunen, <a href="/A231723/b231723.txt">Table of n, a(n) for n = 0..3149</a>
%F a(n) = A219666(n) - A219653(n).
%F A219654(n) = a(n) + A231724(n) + 1.
%o (Scheme)
%o (define (A231723 n) (- (A219666 n) (A219653 n)))
%Y Cf. A231724, A230409, A219662 & A219663.
%K nonn
%O 0,6
%A _Antti Karttunen_, Nov 13 2013