A230416 The infinite trunk of factorial beanstalk (A219666) with reversed subsections.

0, 1, 5, 2, 23, 17, 12, 10, 7, 119, 109, 102, 97, 92, 85, 79, 74, 70, 63, 57, 52, 48, 46, 40, 35, 30, 28, 25, 719, 704, 693, 680, 670, 658, 648, 641, 630, 623, 612, 605, 597, 584, 574, 562, 552, 545, 534, 527, 516, 509, 501, 492, 486, 481, 476, 465, 455, 443

Offset

0,3

Comments

Can be viewed also as an irregular table: after the initial zero on row 0, start each row n with (n!)-1 and subtract repeatedly the sum of factorial expansion digits (A034968) to get successive terms, until the number that has already been listed [which is always (n-1)!-1] is encountered, which is not listed second time, but instead, the current row is finished and the next row starts with ((n+1)!-1), with the same process repeated.

Contains the terms in the infinite trunk of factorial beanstalk (A219666) listed in partially reversed manner: after the initial zero each subsequence lists A219661(n) successive terms from A219666, descending from (n!)-1 downwards.

Links

Antti Karttunen, Rows 0..7, flattened

Formula

For n < 3, a(n) = (n+1)!-1, and for n >= 3, a(n) = (k+2)!-1 if A219651(a(n-1)) is of form k!-1, otherwise just A219651(a(n-1)).

a(n) = A219666(A230432(n)). [Consequence of the definitions]

Example

This irregular table begins as:
0;
1;
5, 2;
23, 17, 12, 10, 7;
119, 109, 102, 97, 92, 85, 79, 74, 70, 63, 57, 52, 48, 46, 40, 35, 30, 28, 25;
...
After the initial zero (on row 0), each row n is A219661(n) elements long.

Prog

(Scheme, with Antti Karttunen's IntSeq-library for memoizing definec-macro)
(definec (A230416 n) (cond ((< n 3) (- (A000142 (+ 1 n)) 1)) ((A219651 (A230416 (-1+ n))) => (lambda (next) (cond ((which_in_A000142? (+ 1 next)) => (lambda (k) (- (A000142 (+ k 2)) 1))) (else next))))))
(define (which_in_A000142? n) (and (> n 0) (let loop ((n n) (i 2)) (cond ((= 1 n) (- i 1)) ((not (zero? (modulo n i))) #f) (else (loop (/ n i) (1+ i)))))))

Crossrefs

Cf. A219666, A219661, A000142, A219651.

The rows are the initial portions of every (n!-1)th row in A219659.

Analogous sequence for binary system: A218616.

Sequence in context: A246798 A367675 A372063 * A363585 A034079 A090882

Adjacent sequences: A230413 A230414 A230415 * A230417 A230418 A230419

Keyword

nonn,tabf

Author

Antti Karttunen, Oct 22 2013

Status

approved