A243346 a(1) = 1, a(2n) = A005117(1+a(n)), a(2n+1) = A013929(a(n)), where A005117 are squarefree and A013929 are nonsquarefree numbers.

1, 2, 4, 3, 8, 6, 12, 5, 9, 13, 24, 10, 18, 19, 32, 7, 16, 14, 25, 21, 36, 38, 63, 15, 27, 30, 49, 31, 50, 53, 84, 11, 20, 26, 45, 22, 40, 39, 64, 34, 54, 59, 96, 62, 99, 103, 162, 23, 44, 42, 72, 47, 80, 79, 126, 51, 81, 82, 128, 86, 136, 138, 220, 17, 28, 33, 52, 41, 68, 73, 120

Offset

1,2

Comments

This permutation entangles complementary pair A005843/A005408 (even/odd numbers) with complementary pair A005117/A013929 (numbers which are squarefree/are not squarefree).

Links

Antti Karttunen, Table of n, a(n) for n = 1..8189

Index entries for sequences that are permutations of the natural numbers

Formula

a(1) = 1, a(2n) = A005117(1+a(n)), a(2n+1) = A013929(a(n)).

For all n > 1, A008966(a(n)) = A000035(n+1), or equally, mu(a(n)) + 1 = n modulo 2, where mu is Moebius mu (A008683). [A property shared with a simpler variant A075378].

Prog

(Scheme) ;; With memoizing macro definec from Antti Karttunen's IntSeq-library.
(definec (A243346 n) (cond ((<= n 1) n) ((even? n) (A005117 (+ 1 (A243346 (/ n 2))))) (else (A013929 (A243346 (/ (- n 1) 2))))))

Crossrefs

Inverse: A243345.

Cf. A005843, A005408, A008966, A005117, A013929, A013928, A057627.

Similar permutations: A075378, A243343-A243344, A243347, A243287-A243288, A135141-A227413, A237126-A237427, A193231.

Sequence in context: A253563 A294044 A243072 * A295029 A338918 A329605

Adjacent sequences: A243343 A243344 A243345 * A243347 A243348 A243349

Keyword

nonn

Author

Antti Karttunen, Jun 03 2014

Status

approved