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A243053 Integer sequence induced by third order Bulgarian solitaire operation on partition list A241918: a(n) = A241909(A243073(A241909(n))). 6
1, 2, 4, 3, 8, 6, 16, 5, 9, 12, 32, 10, 64, 24, 18, 7, 128, 15, 256, 20, 36, 48, 512, 55, 27, 96, 25, 40, 1024, 30, 2048, 49, 72, 192, 54, 21, 4096, 384, 144, 637, 8192, 60, 16384, 80, 50, 768, 32768, 22, 81, 45, 288, 160, 65536, 35, 108, 22627, 576, 1536, 131072 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

The usual (first order) Bulgarian Solitaire operation (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 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.

Similarly, in "Third Order Bulgarian Solitaire Operation", we apply the Second Order Bulgarian operation to the remaining partition (after we have subtracted one from each part) before adding a new part as large as there were parts in the original partition.

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

LINKS

Antti Karttunen, Table of n, a(n) for n = 1..1024

FORMULA

a(n) = A241909(A243073(A241909(n))).

PROG

(Scheme)

(define (A243053 n) (explist->n (ascpart_to_prime-exps (bulgarian-operation-n-th-order (prime-exps_to_ascpart (primefacs->explist n)) 3))))

(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

Third row of A243060.

Differs from A122111 for the first time at n=24, where a(24) = 55, while A122111(24) = 14.

Cf. A243051, A243052, A241918, A241909, A243073.

Sequence in context: A279352 A279351 A122111 * A243052 A153212 A244981

Adjacent sequences:  A243050 A243051 A243052 * A243054 A243055 A243056

KEYWORD

nonn

AUTHOR

Antti Karttunen, May 29 2014

STATUS

approved

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Last modified January 16 06:59 EST 2019. Contains 319188 sequences. (Running on oeis4.)