

A334727


Binary interpretation of the left diagonal of the XORtriangle with first row generated from the binary expansion of n, with most significant bit given by first row.


4



0, 1, 3, 2, 7, 6, 5, 4, 15, 14, 12, 13, 10, 11, 9, 8, 31, 30, 29, 28, 25, 24, 27, 26, 21, 20, 23, 22, 19, 18, 17, 16, 63, 62, 60, 61, 59, 58, 56, 57, 51, 50, 48, 49, 55, 54, 52, 53, 42, 43, 41, 40, 46, 47, 45, 44, 38, 39, 37, 36, 34, 35, 33, 32, 127, 126, 125
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OFFSET

0,3


COMMENTS

This sequence is a selfinverse permutation of the nonnegative numbers, with only two fixed points: a(0) = 0 and a(1) = 1.


LINKS

Rémy Sigrist, Table of n, a(n) for n = 0..8191
Index entries for sequences related to binary expansion of n
Index entries for sequences related to XORtriangles
Index entries for sequences that are permutations of the natural numbers


FORMULA

a(floor(n/2)) = floor(a(n)/2).
abs(a(2*n+1)  a(2*n)) = 1.
a(2^k) = 2^(k+1)  1 for any k >= 0.
a(2^k1) = 2^(k1) for any k > 0.


EXAMPLE

For n = 42:
 the binary expansion of 42 is "101010",
 the corresponding XORtriangle is:
1 0 1 0 1 0
1 1 1 1 1
0 0 0 0
0 0 0
0 0
0
 the bits on the left diagonal are: 1, 1, 0, 0, 0, 0,
 so a(42) = 2^5 + 2^4 = 48.


PROG

(PARI) a(n) = { my (v=0); forstep (x=#binary(n)1, 0, 1, if (bittest(n, x), v+=2^x; ); n=bitxor(n, n\2)); return (v) }


CROSSREFS

See A334595 for a similar sequence.
Sequence in context: A083569 A071574 A276344 * A276343 A054429 A269398
Adjacent sequences: A334724 A334725 A334726 * A334728 A334729 A334730


KEYWORD

nonn,base


AUTHOR

Rémy Sigrist, May 09 2020


STATUS

approved



