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A260434 Permutation of natural numbers: a(1) = 1, a(2n) = A257803(1+a(n)), a(2n+1) = A257804(a(n)), where A257803 and A257804 give the positions of odd and even terms in A233271, the infinite trunk of inverted binary beanstalk. 4
1, 4, 2, 12, 6, 7, 3, 30, 19, 18, 10, 21, 11, 9, 5, 74, 48, 52, 32, 49, 31, 25, 15, 54, 36, 27, 16, 24, 14, 17, 8, 172, 125, 118, 85, 128, 89, 76, 51, 119, 86, 75, 50, 64, 43, 38, 26, 132, 92, 83, 61, 68, 45, 41, 28, 60, 40, 35, 22, 42, 29, 23, 13, 383, 314, 275, 219, 266, 208, 201, 152, 283, 227, 207, 159, 174, 129, 127, 88 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

This sequence can be represented as a binary tree. Each left hand child is produced as A257803(1+n), and each right hand child as A257804(n), when the parent contains n:

                                     |

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

                 4                                       2

      12......../ \........6                   7......../ \........3

      / \                 / \                 / \                 / \

     /   \               /   \               /   \               /   \

    /     \             /     \             /     \             /     \

  30       19         18       10         21       11          9       5

74  48   52  32     49  31   25  15     54  36   27  16      24 14   17 8

etc.

Note how this is a mirror image of the tree shown in A260432.

LINKS

Antti Karttunen, Table of n, a(n) for n = 1..16383

Index entries for sequences that are permutations of the natural numbers

FORMULA

a(1) = 1, a(2n) = A257803(1+a(n)), a(2n+1) = A257804(a(n)).

As a composition of other permutations:

a(n) = A260432(A054429(n)).

a(n) = A260430(A260432(n)).

PROG

(Scheme, with memoizing macro definec)

(definec (A260434 n) (cond ((<= n 1) n) ((even? n) (A257803 (+ 1 (A260434 (/ n 2))))) (else (A257804 (A260434 (/ (- n 1) 2))))))

CROSSREFS

Inverse: A260433.

Related permutations: A260432, A260430, A054429.

Cf. A257803, A257804, A257807, A257808.

Cf. also A233271, A257806.

Sequence in context: A077015 A077016 A191436 * A243344 A293603 A201825

Adjacent sequences:  A260431 A260432 A260433 * A260435 A260436 A260437

KEYWORD

nonn,tabf,look

AUTHOR

Antti Karttunen, Jul 27 2015

STATUS

approved

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Last modified December 6 18:03 EST 2019. Contains 329809 sequences. (Running on oeis4.)