

A264596


Let S_n be the list of the first n nonnegative numbers written in binary, with least significant bits on the left, and sorted into lexicographic order; a(n) = position of n in S_n, starting indexing at 0.


6



0, 1, 1, 3, 1, 4, 3, 7, 1, 6, 4, 10, 3, 10, 7, 15, 1, 10, 6, 16, 4, 15, 10, 22, 3, 16, 10, 24, 7, 22, 15, 31, 1, 18, 10, 28, 6, 25, 16, 36, 4, 25, 15, 37, 10, 33, 22, 46, 3, 28, 16, 42, 10, 37, 24, 52, 7, 36, 22, 52, 15, 46, 31, 63, 1, 34, 18, 52, 10, 45, 28
(list;
graph;
refs;
listen;
history;
text;
internal format)



OFFSET

0,4


LINKS

Alois P. Heinz, Table of n, a(n) for n = 0..20000


FORMULA

a(2^n) = 1.
a(2^n1) = 2^n1.
a(2n) = a(n), a(2n+1) = a(n) + n+1, a(0) = 0.  Alois P. Heinz, Nov 19 2015
Conjecture: a(n) = n*(n + 3)/2  A007814(A293290(n)) for n > 0.  Velin Yanev, Sep 12 2017


EXAMPLE

S_0 = [0], a(0) = 0;
S_1 = [0, 1], a(1) = 1;
S_2 = [0, 01, 1], a(2) = 1;
S_3 = [0, 01, 1, 11], a(3) = 3;
S_4 = [0, 001, 01, 1, 11], a(4) = 1;
S_5 = [0, 001, 01, 1, 101, 11], a(5) = 4;
S_6 = [0, 001, 01, 011, 1, 101, 11], a(6) = 3;
S_7 = [0, 001, 01, 011, 1, 101, 11, 111], a(7) = 7;
S_8 = [0, 0001, 001, 01, 011, 1, 101, 11, 111], a(8) = 1;
...


MAPLE

a:= proc(n) option remember; `if`(n=0, 0,
`if`(irem(n, 2, 'r')=0, a(r), a(r)+r+1))
end:
seq(a(n), n=0..100); # Alois P. Heinz, Nov 19 2015


PROG

(Python)
def A264596(n):
return sorted(format(i, 'b')[::1] for i in range(n+1)).index(format(n, 'b')[::1]) # Chai Wah Wu, Nov 22 2015


CROSSREFS

Suggested by John Bodeen's A263856.
Cf. A188215.
Sequence in context: A054019 A230877 A209613 * A262214 A035626 A082587
Adjacent sequences: A264593 A264594 A264595 * A264597 A264598 A264599


KEYWORD

nonn,base


AUTHOR

N. J. A. Sloane, Nov 19 2015


EXTENSIONS

More terms from Alois P. Heinz, Nov 19 2015


STATUS

approved



