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A243052 Integer sequence induced by second order Bulgarian solitaire operation on partition list A241918: a(n) = A241909(A243072(A241909(n))).

%I A243052 #9 Nov 02 2014 12:18:37
%S A243052 1,2,4,3,8,6,16,5,9,12,32,35,64,24,18,25,128,15,256,539,36,48,512,14,
%T A243052 27,96,25,17303,1024,175,2048,125,72,192,54,21,4096,384,144,154,8192,
%U A243052 3773,16384,485537,245,768,32768,70,81,45,288,26977283,65536,10,108,3146,576,1536,131072
%N A243052 Integer sequence induced by second order Bulgarian solitaire operation on partition list A241918: a(n) = A241909(A243072(A241909(n))).
%C A243052 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.
%C A243052 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.
%C A243052 How the partitions are encoded in this case, please see A241918.
%H A243052 Antti Karttunen, <a href="/A243052/b243052.txt">Table of n, a(n) for n = 1..512</a>
%F A243052 a(n) = A241909(A243072(A241909(n))).
%o A243052 (Scheme)
%o A243052 (define (A243052 n) (explist->n (ascpart_to_prime-exps (bulgarian-operation-n-th-order (prime-exps_to_ascpart (primefacs->explist n)) 2))))
%o A243052 (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))))))))
%o A243052 ;; Other required functions and libraries, please see A243051.
%Y A243052 Second row of A243060.
%Y A243052 Cf. A243051, A243053, A241918, A241909, A243072.
%K A243052 nonn
%O A243052 1,2
%A A243052 _Antti Karttunen_, May 29 2014