

A330081


If the binary expansion of n is (b(1), ..., b(w)), then the binary expansion of a(n) is (b(1), b(3), b(5), ..., b(6), b(4), b(2)).


5



0, 1, 2, 3, 4, 6, 5, 7, 8, 10, 12, 14, 9, 11, 13, 15, 16, 20, 18, 22, 24, 28, 26, 30, 17, 21, 19, 23, 25, 29, 27, 31, 32, 36, 40, 44, 34, 38, 42, 46, 48, 52, 56, 60, 50, 54, 58, 62, 33, 37, 41, 45, 35, 39, 43, 47, 49, 53, 57, 61, 51, 55, 59, 63, 64, 72, 68, 76
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OFFSET

0,3


COMMENTS

This sequence is a permutation of the nonnegative integers that preserves the binary length as well as the Hamming weight. See A330090 for the inverse.


LINKS

Rémy Sigrist, Table of n, a(n) for n = 0..8192
Index entries for sequences related to binary expansion of n
Index entries for sequences that are permutations of the natural numbers


FORMULA

If n has w binary digits, then a^A003558(w1)(n) = n (where a^k denotes the kth iterate of the sequence).


EXAMPLE

For n = 1234:
 the binary expansion of 1234 is "10011010010",
 oddindexed bits are "101100",
 evenindexed bits are "01001", and in reverse order "10010",
 hence the binary expansion of a(1234) is "10110010010",
 so a(1234) = 1426.


PROG

(PARI) shuffle(v) = { my (w=vector(#v), o=0, e=#v+1); for (k=1, #v, w[if (k%2, o++, e)]=v[k]); w }
a(n) = fromdigits(shuffle(binary(n)), 2)


CROSSREFS

See A329303 for a similar sequence.
Cf. A003558, A194959, A330090 (inverse).
Sequence in context: A275119 A218252 A080541 * A072759 A361482 A257683
Adjacent sequences: A330078 A330079 A330080 * A330082 A330083 A330084


KEYWORD

nonn,base,easy


AUTHOR

Rémy Sigrist, Dec 01 2019


STATUS

approved



