A243288 - OEIS

A243288

Permutation of natural numbers: a(1)=1, a(2n) = A102750(a(n)), a(2n+1) = A070003(a(n)).

1, 2, 4, 3, 8, 6, 16, 5, 9, 12, 32, 10, 25, 22, 81, 7, 18, 13, 36, 17, 54, 42, 242, 14, 49, 34, 150, 30, 128, 99, 882, 11, 27, 24, 100, 19, 64, 46, 256, 23, 98, 68, 490, 55, 338, 279, 4624, 20, 72, 62, 432, 44, 245, 178, 2209, 40, 216, 154, 1800, 119, 1200, 966

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OFFSET

1,2

COMMENTS

This is an instance of "entanglement permutation", where two pairs of complementary subsets of natural numbers are interwoven with each other. In this case complementary pair odd/even numbers (A005408/A005843) is entangled with complementary pair A070003/A102750 (numbers which are divisible/not divisible by the square of their largest prime factor).

Thus this shares with the permutation A122111 the property that each even number is mapped to a unique term of A102750 and each odd number (larger than 1) to a unique term of A070003.

LINKS

Antti Karttunen, Table of n, a(n) for n = 1..94

Index entries for sequences that are permutations of the natural numbers

FORMULA

a(1)=1, and for n > 1, if n=2k, a(n) = A102750(a(k)), otherwise, when n = 2k+1, a(n) = A070003(a(k)).

PROG

(Scheme, with Antti Karttunen's IntSeq-library)

(definec (A243288 n) (cond ((<= n 1) n) ((even? n) (A102750 (A243288 (/ n 2)))) (else (A070003 (A243288 (/ (- n 1) 2))))))

CROSSREFS

Inverse of A243287.

Cf. A005843, A005408, A070003, A102750, A243282, A243285, A241917, A122111.

Similarly constructed permutations: A243343-A243346, A135141-A227413, A237126-A237427, A193231.