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A230416
The infinite trunk of factorial beanstalk (A219666) with reversed subsections.
5
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
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
KEYWORD
nonn,tabf
AUTHOR
Antti Karttunen, Oct 22 2013
STATUS
approved