OFFSET
1,2
COMMENTS
This sequence is closed with respect to A122111, i.e., for any n, A122111(a(n)) is either the same as a(n) or some other term a(k) of the sequence.
These numbers encode partitions in whose Young diagrams all pairs of successive horizontal and vertical segments (those pairs sharing "a common convex corner") are of equal length. Cf. the example-illustration at A153212.
Note: The seventh primorial, 510510 (= A002110(7)) occurs here as a term a(62).
EXAMPLE
2 = p_1^1 is present, as the first prime index delta and exponent are equal.
3 = p_2^1 is not present, as 1 <> 2.
6 = p_1^1 * p_2^(2-1) is present.
9 = p_2^2 is present, as 2 = 2.
30 = p_1^1 * p_2^(2-1) * p_3^(3-2) is present, as all primorials are.
50 = p_1^1 * p_3^(3-1) is present also.
PROG
(Scheme) ;; With Antti Karttunen's IntSeq-library.
;; The following is a faster version, but gives the terms in non-monotone order. Note that its indexing starts from zero.
;; A000975 gives the positions where primorials occur, after which only larger terms occur, use this fact for selecting a prefix sequence of appropriate length before sorting.
(define (A242421_in_wrong_order n) (let ((complist (binexp->runcount1list n))) (apply * (map (lambda (i e) (expt (A000040 i) e)) (partsums complist) complist))))
;; For the function binexp->runcount1list and partsums, see for example A129594.
CROSSREFS
KEYWORD
nonn
AUTHOR
Antti Karttunen, May 16 2014
STATUS
approved
