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A255566 a(0) = 0; after which, a(2n) = A255411(a(n)), a(2n+1) = A256450(a(n)). 7
0, 1, 4, 2, 18, 6, 12, 3, 96, 24, 48, 8, 72, 15, 16, 5, 600, 120, 240, 30, 360, 56, 60, 10, 480, 87, 88, 20, 90, 21, 22, 7, 4320, 720, 1440, 144, 2160, 270, 288, 36, 2880, 416, 420, 67, 432, 73, 66, 13, 3600, 567, 568, 107, 570, 109, 108, 26, 576, 111, 112, 27, 114, 28, 52, 9, 35280, 5040, 10080, 840, 15120, 1584, 1680, 168 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

This sequence can be represented as a binary tree. Each left hand child is produced as A255411(n), and each right hand child as A256450(n), when parent contains n >= 1:

                                      0

                                      |

                   ...................1...................

                  4                                       2

       18......../ \........6                  12......../ \........3

       / \                 / \                 / \                 / \

      /   \               /   \               /   \               /   \

     /     \             /     \             /     \             /     \

   96       24         48       8          72       15         16       5

600  120 240  30    360  56   60 10     480  87   88  20     90  21   22 7

etc.

Because all terms of A255411 are even it means that odd terms can occur only in odd positions (together with some even terms, for each one of which there is a separate infinite cycle), while terms in even positions are all even.

After its initial 1, A255567 seems to give all the terms like 2, 3, 12, ... where the left hand child of the right hand child is one more than the right hand child of the left hand child (as for 2: 16 = 15+1, as for 3: 22 = 21+1, as for 12: 88 = 87+1).

LINKS

Antti Karttunen, Table of n, a(n) for n = 0..1023

Index entries for sequences related to factorial base representation

Index entries for sequences that are permutations of the natural numbers

FORMULA

a(0) = 0; after which, a(2n) = A255411(a(n)), a(2n+1) = A256450(a(n)).

Other identities:

For all n >= 0, a(2^n) = A001563(n+1). [The leftmost branch of the binary tree is given by n*n!]

For all n >= 0, a(A083318(n)) = A000142(n+1). [And the next innermost vertices by (n+1)! This follows because A256450(n*n! - 1) = (n+1)! - 1.]

For all n >= 1, A257679(a(n)) = A001511(n).

PROG

(Scheme, with memoization-macro definec)

(definec (A255566 n) (cond ((zero? n) n) ((even? n) (A255411 (A255566 (/ n 2)))) (else (A256450 (A255566 (/ (- n 1) 2))))))

CROSSREFS

Inverse: A255565.

Cf. A000142, A001511, A001563, A083318, A255411, A256450, A257679.

Cf. also A255567 and arrays A257503, A257505.

Related or similar permutations: A273666, A273667.

Sequence in context: A303142 A328695 A285595 * A302461 A303243 A074676

Adjacent sequences:  A255563 A255564 A255565 * A255567 A255568 A255569

KEYWORD

nonn,base,tabf

AUTHOR

Antti Karttunen, May 05 2015

EXTENSIONS

Formula changed because of the changed starting offset of A256450 - Antti Karttunen, May 30 2016

STATUS

approved

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Last modified August 5 06:18 EDT 2021. Contains 346457 sequences. (Running on oeis4.)