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A243052 Integer sequence induced by second order Bulgarian solitaire operation on partition list A241918: a(n) = A241909(A243072(A241909(n))). 6
1, 2, 4, 3, 8, 6, 16, 5, 9, 12, 32, 35, 64, 24, 18, 25, 128, 15, 256, 539, 36, 48, 512, 14, 27, 96, 25, 17303, 1024, 175, 2048, 125, 72, 192, 54, 21, 4096, 384, 144, 154, 8192, 3773, 16384, 485537, 245, 768, 32768, 70, 81, 45, 288, 26977283, 65536, 10, 108, 3146, 576, 1536, 131072 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

The usual Bulgarian Solitaire operation (the "first order" version, cf. A243051) applied to an unordered integer partition means: subtract one from each part, and add a new part as large as there were parts in the old partition.

The "Second Order Bulgarian Solitaire" operation means that after subtracting one from each part of the old partition (and discarding the parts that diminished to zero), we apply the (first order) Bulgarian operation to the remaining partition before adding a new part as large as there were parts in the original partition.

How the partitions are encoded in this case, please see A241918.

LINKS

Antti Karttunen, Table of n, a(n) for n = 1..512

FORMULA

a(n) = A241909(A243072(A241909(n))).

PROG

(Scheme)

(define (A243052 n) (explist->n (ascpart_to_prime-exps (bulgarian-operation-n-th-order (prime-exps_to_ascpart (primefacs->explist n)) 2))))

(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))))))))

;; Other required functions and libraries, please see A243051.

CROSSREFS

Second row of A243060.

Cf. A243051, A243053, A241918, A241909, A243072.

Sequence in context: A279351 A122111 A243053 * A153212 A244981 A284571

Adjacent sequences:  A243049 A243050 A243051 * A243053 A243054 A243055

KEYWORD

nonn

AUTHOR

Antti Karttunen, May 29 2014

STATUS

approved

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Last modified January 22 22:38 EST 2018. Contains 298093 sequences.