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A243071 Permutation of nonnegative integers: a(1) = 0, a(2) = 1, a(2n) = 2*a(n), a(2n+1) = 1 + 2*a(A064989(2n+1)). 52
0, 1, 3, 2, 7, 6, 15, 4, 5, 14, 31, 12, 63, 30, 13, 8, 127, 10, 255, 28, 29, 62, 511, 24, 11, 126, 9, 60, 1023, 26, 2047, 16, 61, 254, 27, 20, 4095, 510, 125, 56, 8191, 58, 16383, 124, 25, 1022, 32767, 48, 23, 22, 253, 252, 65535, 18, 59, 120, 509, 2046, 131071 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

COMMENTS

Note the indexing: the domain starts from 1, while the range includes also zero.

See also the comments at A163511, which is the inverse permutation to this one.

LINKS

Antti Karttunen, Table of n, a(n) for n = 1..1024

Index entries for sequences that are permutations of the natural numbers

FORMULA

a(1) = 0, a(2) = 1, a(2n) = 2*a(n), a(2n+1) = 1 + 2*a(A064989(2n+1)).

For n >= 1, a(A000040(n)) = A000225(n).

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

PROG

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

(definec (A243071 n) (cond ((<= n 2) (- n 1)) ((even? n) (* 2 (A243071 (/ n 2)))) (else (+ 1 (* 2 (A243071 (A064989 n)))))))

(Python)

from functools import reduce

from sympy import factorint, prevprime

from operator import mul

def a064989(n):

    f = factorint(n)

    return 1 if n==1 else reduce(mul, (1 if i==2 else prevprime(i)**f[i] for i in f))

def a(n): return n - 1 if n<3 else 2*a(n//2) if n%2==0 else 1 + 2*a(a064989(n))

print([a(n) for n in range(1, 101)]) # Indranil Ghosh, Jun 15 2017

CROSSREFS

Inverse: A163511.

Cf. A000040, A000225, A064989, A064216.

Sequence in context: A056481 A269386 A252756 * A332811 A286556 A243354

Adjacent sequences:  A243068 A243069 A243070 * A243072 A243073 A243074

KEYWORD

nonn

AUTHOR

Antti Karttunen, Jun 20 2014

STATUS

approved

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Last modified May 24 18:33 EDT 2020. Contains 334580 sequences. (Running on oeis4.)