A360287 a(n) is the concatenation of the positions of 1-bits in the binary expansion of the Gray code for n, when 1 is the rightmost position; a(0) = 0.

0, 1, 12, 2, 23, 123, 13, 3, 34, 134, 1234, 234, 24, 124, 14, 4, 45, 145, 1245, 245, 2345, 12345, 1345, 345, 35, 135, 1235, 235, 25, 125, 15, 5, 56, 156, 1256, 256, 2356, 12356, 1356, 356, 3456, 13456, 123456, 23456, 2456, 12456, 1456, 456, 46, 146, 1246, 246

Offset

0,3

Comments

a(n) represents the n-th finite subset of positive integers in Gray order, two consecutive sets differ in exactly one member: {}, {1}, {1,2}, {2}, {2,3}, {1,2,3}, {1,3}, {3}, {3,4}, {1,3,4}, {1,2,3,4}, {2,3,4}, ... .

a(n) is the concatenation of all terms in the n-th row of A227738 (for n>=1).

Links

Alois P. Heinz, Table of n, a(n) for n = 0..16383

Wikipedia, Gray code

Formula

a(2^n-1) = a(A000225(n)) = n.

a(floor(2^(n+1)/3)) = a(A000975(n)) = A007908(n).

Example

A003188(17) = 25 = 11001_2 gives a(17) = 145.

Maple

a:= n-> `if`(n=0, 0, (l-> parse(cat(seq(`if`(l[i]=1, i, [][]),
     i=1..nops(l)))))(Bits[Split](Bits[Xor](n, iquo(n, 2))))):
seq(a(n), n=0..100);

Crossrefs

Cf. A000225, A000975, A003188, A007908, A048794, A227738.

Sequence in context: A303782 A375462 A335043 * A040143 A163599 A334700

Adjacent sequences: A360284 A360285 A360286 * A360288 A360289 A360290

Keyword

nonn,look,base

Author

Alois P. Heinz, Feb 01 2023

Status

approved