A243344 - OEIS

A243344

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

1, 4, 2, 12, 6, 8, 3, 32, 19, 18, 10, 24, 13, 9, 5, 84, 53, 50, 31, 49, 30, 27, 15, 63, 38, 36, 21, 25, 14, 16, 7, 220, 138, 136, 86, 128, 82, 81, 51, 126, 79, 80, 47, 72, 42, 44, 23, 162, 103, 99, 62, 96, 59, 54, 34, 64, 39, 40, 22, 45, 26, 20, 11, 564, 365

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OFFSET

1,2

COMMENTS

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

LINKS

Antti Karttunen, Table of n, a(n) for n = 1..4095

Index entries for sequences that are permutations of the natural numbers

FORMULA

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

For all n, A008966(a(n)) = A000035(n), or equally, mu(a(n)) = n modulo 2, where mu is Moebius mu (A008683). [The same property holds for A088610.]

PROG

(Scheme, with memoizing definec-macro from Antti Karttunen's IntSeq-library)

(definec (A243344 n) (cond ((<= n 1) n) ((even? n) (A013929 (A243344 (/ n 2)))) (else (A005117 (+ 1 (A243344 (/ (- n 1) 2)))))))

CROSSREFS

Inverse: A243343.

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