A245605 Permutation of natural numbers: a(1) = 1, a(2n) = 2 * a(A064989(2n-1)), a(2n-1) = 1 + (2 * a(A064989(2n-1)-1)).

1, 2, 3, 4, 5, 6, 9, 10, 7, 8, 13, 18, 17, 26, 11, 12, 37, 34, 25, 74, 15, 16, 69, 50, 21, 14, 19, 20, 33, 138, 41, 66, 35, 52, 53, 22, 277, 82, 31, 32, 45, 554, 65, 90, 27, 36, 1109, 130, 101, 42, 43, 28, 73, 2218, 149, 30, 71, 104, 57, 146, 209, 114, 51, 148, 133, 70, 293, 418, 555, 164, 141, 586, 329, 282, 75, 68, 105, 106, 1173, 658, 23, 24

Offset

1,2

Comments

The even bisection halved gives A245607. The odd bisection incremented by one and halved gives A245707.

Links

Antti Karttunen, Table of n, a(n) for n = 1..10001

Index entries for sequences that are permutations of the natural numbers

Formula

a(1) = 1, a(2n) = 2 * a(A064989(2n-1)), a(2n-1) = 1 + (2 * a(A064989(2n-1)-1)).

a(1) = 1, a(2n) = 2 * a(A064216(n)), a(2n-1) = 1 + (2 * a(A064216(n)-1)).

As a composition of related permutations:

a(n) = A245607(A048673(n)).

Prog

(PARI)
A064989(n) = my(f = factor(n)); for(i=1, #f~, if((2 == f[i, 1]), f[i, 1] = 1, f[i, 1] = precprime(f[i, 1]-1))); factorback(f);
A245605(n) = if(1==n, 1, if(0==(n%2), 2*A245605(A064989(n-1)), 1+(2*A245605(A064989(n)-1))));
for(n=1, 10001, write("b245605.txt", n, " ", A245605(n)));
(Scheme, with memoization-macro definec)
(definec (A245605 n) (cond ((= 1 n) 1) ((even? n) (* 2 (A245605 (A064989 (- n 1))))) (else (+ 1 (* 2 (A245605 (-1+ (A064989 n))))))))

Crossrefs

Inverse: A245606.

Cf. A048673, A064216, A064989, A245607, A245705, A245707.

Similar entanglement permutations: A244319, A005940, A163511, A243287, A243343, A243345, A244321, A245603, A245613, A135141, A237427.

Sequence in context: A240827 A023841 A340553 * A269863 A297165 A245606

Adjacent sequences: A245602 A245603 A245604 * A245606 A245607 A245608

Keyword

nonn

Author

Antti Karttunen, Jul 29 2014

Status

approved