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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^n-1) = 2^n-1.

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

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Last modified February 18 03:43 EST 2018. Contains 299298 sequences. (Running on oeis4.)