A269171 - OEIS

A269171

Permutation of natural numbers: a(1) = 1, a(2n) = 2*a(n), a(2n+1) = A269379(a(A268674(2n+1))).

1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 23, 20, 21, 22, 25, 24, 19, 26, 27, 28, 29, 30, 37, 32, 33, 34, 35, 36, 41, 46, 39, 40, 43, 42, 47, 44, 45, 50, 53, 48, 31, 38, 51, 52, 61, 54, 49, 56, 57, 58, 67, 60, 71, 74, 63, 64, 65, 66, 77, 68, 69, 70, 83, 72, 89, 82, 75, 92, 59, 78, 91, 80, 81, 86, 97, 84, 79, 94, 87, 88, 107, 90, 85, 100

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,2

LINKS

Antti Karttunen, Table of n, a(n) for n = 1..8192

Index entries for sequences that are permutations of the natural numbers

FORMULA

a(1) = 1, then after for even n, a(n) = 2*a(n/2), and for odd n, a(n) = A269379(a(A268674(n))).

a(1) = 1, for n > 1, a(n) = A255127(A055396(n), a(A078898(n))).

As a composition of other permutations:

a(n) = A269385(A252756(n)).

a(n) = A269387(A252754(n)).

Other identities. For all n >= 1:

A000035(a(n)) = A000035(n). [Preserves the parity of n.]

a(A008578(n)) = A003309(n). [Maps noncomposites to Ludic numbers.]

PROG

(Scheme, two versions, both using memoization-macro definec)

(definec (A269171 n) (cond ((<= n 1) n) ((even? n) (* 2 (A269171 (/ n 2)))) (else (A269379 (A269171 (A268674 n))))))

(definec (A269171 n) (if (<= n 1) n (A255127bi (A055396 n) (A269171 (A078898 n))))) ;; Code for A255127bi given in A255127.

CROSSREFS

Inverse: A269172.

Cf. A000035, A003309, A008578, A055396, A078898, A268674, A255127, A269379.

Related or similar permutations: A260741, A260742, A269355, A269357, A255421, A252754, A252756, A269385, A269387.

Cf. also A269393 (a(3n)/3) and A269395.

Differs from A255407 for the first time at n=38, where a(38) = 46, while A255407(38) = 38.

Sequence in context: A261924 A255421 A255407 * A269395 A302025 A269396

Adjacent sequences: A269168 A269169 A269170 * A269172 A269173 A269174

KEYWORD

nonn

AUTHOR

Antti Karttunen, Mar 03 2016

STATUS

approved