A231723 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).

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, 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, 4, 2, 1, 1, 2, 1, 0, 0, 0, 0, 0, 0, 1, 3, 5, 7, 8, 1, 0

Offset

0,6

Comments

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.

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.

Links

Antti Karttunen, Table of n, a(n) for n = 0..3149

Formula

a(n) = A219666(n) - A219653(n).

A219654(n) = a(n) + A231724(n) + 1.

Prog

(Scheme)
(define (A231723 n) (- (A219666 n) (A219653 n)))

Crossrefs

Cf. A231724, A230409, A219662 & A219663.

Sequence in context: A369814 A239928 A114912 * A342720 A029274 A239498

Adjacent sequences: A231720 A231721 A231722 * A231724 A231725 A231726

Keyword

nonn

Author

Antti Karttunen, Nov 13 2013

Status

approved