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

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.

Sequence in context: A243345 A297499 A243287 * A279352 A279351 A122111

Adjacent sequences: A243285 A243286 A243287 * A243289 A243290 A243291

Keyword

nonn

Author

Antti Karttunen, Jun 02 2014

Status

approved