A269172 Permutation of natural numbers: a(1) = 1, a(2n) = 2*a(n), a(2n+1) = A250469(a(A269380(2n+1))).

1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 25, 20, 21, 22, 19, 24, 23, 26, 27, 28, 29, 30, 49, 32, 33, 34, 35, 36, 31, 50, 39, 40, 37, 42, 41, 44, 45, 38, 43, 48, 55, 46, 51, 52, 47, 54, 121, 56, 57, 58, 77, 60, 53, 98, 63, 64, 65, 66, 59, 68, 69, 70, 61, 72, 169, 62, 75, 100, 67, 78, 85, 80, 81

Offset

1,2

Links

Antti Karttunen, Table of n, a(n) for n = 1..2244

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, A250469(a(A269380(n))).

a(1) = 1, for n > 1, a(n) = A083221(A260738(n), a(A260739(n))).

As a composition of other permutations:

a(n) = A252755(A269386(n)).

a(n) = A252753(A269388(n)).

Other identities. For all n >= 1:

A000035(a(n)) = A000035(n). [This permutation preserves the parity of n.]

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

Prog

(Scheme, two versions, both using memoization-macro definec)
(definec (A269172 n) (cond ((<= n 1) n) ((even? n) (* 2 (A269172 (/ n 2)))) (else (A250469 (A269172 (A269380 n))))))
(definec (A269172 n) (if (<= n 1) n (A083221bi (A260738 n) (A269172 (A260739 n))))) ;; Code for A083221bi given in A083221.

Crossrefs

Inverse: A269171.

Cf. A000035, A003309, A008578, A083221, A250469, A260738, A260739, A269380.

Related or similar permutations: A260741, A260742, A269356, A269358, A255422.

Cf. also A269394 (a(3n)/3) and A269396.

Differs from A255408 for the first time at n=38, where a(38) = 50, while A255408(38) = 38.

Sequence in context: A302025 A269396 A255408 * A302026 A358373 A285054

Adjacent sequences: A269169 A269170 A269171 * A269173 A269174 A269175

Keyword

nonn

Author

Antti Karttunen, Mar 03 2016

Status

approved