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.

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

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: A205395 A367647 A243070 * A286321 A349192 A118235

Adjacent sequences: A243057 A243058 A243059 * A243061 A243062 A243063

Keyword

nonn,tabl

Author

Antti Karttunen, May 29 2014

Status

approved