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A243060 Square array read by antidiagonals: rows are successively recursivized versions of Bulgarian solitaire operation (starting from the usual "first order" version, A243051), as applied to partitions listed in A241918. 8
1, 2, 1, 4, 2, 1, 3, 4, 2, 1, 8, 3, 4, 2, 1, 25, 8, 3, 4, 2, 1, 16, 6, 8, 3, 4, 2, 1, 9, 16, 6, 8, 3, 4, 2, 1, 9, 5, 16, 6, 8, 3, 4, 2, 1, 343, 9, 5, 16, 6, 8, 3, 4, 2, 1, 32, 12, 9, 5, 16, 6, 8, 3, 4, 2, 1, 10, 32, 12, 9, 5, 16, 6, 8, 3, 4, 2, 1, 64, 35, 32, 12, 9, 5, 16, 6, 8, 3, 4, 2, 1, 14641, 64, 10, 32, 12, 9, 5, 16, 6, 8, 3, 4, 2, 1, 125, 24, 64, 10, 32, 12, 9, 5, 16, 6, 8, 3, 4, 2, 1 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

The array is read by antidiagonals: A(0,0), A(0,1), A(1,0), A(0,2), A(1,1), A(2,0), ... .

Each row is a A241909-conjugate of the corresponding row in A243070.

Rows in both arrays converge towards A122111.

First point where row k differs from row k of A243070 seems to be A000040(k+2): primes from five onward: 5, 7, 11, 13, 17, 19, 23, 29, 31, ...

While the first point where row k differs from A122111 seems to begin as 6, 12, 24, 48, 96, 192, 384, 768, 1536, 3072, ... A007283 (3*2^n) from the term n=1 onward.

The rows in this table preserve A243503.

LINKS

Table of n, a(n) for n=1..120.

EXAMPLE

The top left corner of the array:

  1, 2, 4, 3, 8, 25, 16, 9, 9, 343,  32,  10,  64, 14641,   125,   27, ...

  1, 2, 4, 3, 8,  6, 16, 5, 9,  12,  32,  35,  64,    24,    18,   25, ...

  1, 2, 4, 3, 8,  6, 16, 5, 9,  12,  32,  10,  64,    24,    18,    7, ...

  1, 2, 4, 3, 8,  6, 16, 5, 9,  12,  32,  10,  64,    24,    18,    7, ...

  1, 2, 4, 3, 8,  6, 16, 5, 9,  12,  32,  10,  64,    24,    18,    7, ...

PROG

(Scheme)

(define (A243060 n) (A243060bi (A002260 n) (A004736 n)))

(define (A243060bi row col) (explist->n (ascpart_to_prime-exps (bulgarian-operation-n-th-order (prime-exps_to_ascpart (primefacs->explist col)) row))))

(define (bulgarian-operation-n-th-order ascpart n) (if (or (zero? n) (null? ascpart)) ascpart (let ((newpart (length ascpart))) (let loop ((newpartition (list)) (ascpart ascpart)) (cond ((null? ascpart) (sort (cons newpart (bulgarian-operation-n-th-order newpartition (- n 1))) <)) (else (loop (if (= 1 (car ascpart)) newpartition (cons (- (car ascpart) 1) newpartition)) (cdr ascpart))))))))

;; For other required functions and libraries, please see A243051.

CROSSREFS

Row 1: A243051, Row 2: A243052, Row 3: A243053.

Rows converge towards A122111.

Cf. A243070, A243503.

Sequence in context: A268267 A205395 A243070 * A286321 A118235 A304624

Adjacent sequences:  A243057 A243058 A243059 * A243061 A243062 A243063

KEYWORD

nonn,tabl

AUTHOR

Antti Karttunen, May 29 2014

STATUS

approved

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Last modified January 23 02:57 EST 2019. Contains 319368 sequences. (Running on oeis4.)