A346306 Position in A076478 of the binary complement of the n-th word in A076478.

2, 1, 6, 5, 4, 3, 14, 13, 12, 11, 10, 9, 8, 7, 30, 29, 28, 27, 26, 25, 24, 23, 22, 21, 20, 19, 18, 17, 16, 15, 62, 61, 60, 59, 58, 57, 56, 55, 54, 53, 52, 51, 50, 49, 48, 47, 46, 45, 44, 43, 42, 41, 40, 39, 38, 37, 36, 35, 34, 33, 32, 31, 126, 125, 124, 123

Offset

1,1

Comments

Permutation of the positive integers obtained by reversing their order within successive subsets of length 2, 4, 8, 16, ... - Paolo Xausa, Mar 09 2023

Links

Michael S. Branicky, Table of n, a(n) for n = 1..16382 (for all words with length <= 13)

Index entries for sequences that are permutations of the natural numbers

Formula

a(n) = 3*(2^d - 1) - n, where 2^d - 1 <= n <= 2^(d+1) - 2. - Michael S. Branicky, Sep 03 2021

Example

The first fourteen words w(n) are 0, 1, 00, 01, 10, 11, 000, 001, 010, 011, 100, 101, 110, 111, so that a(3) = 6.
From Paolo Xausa, Mar 09 2023: (Start)
Written as an irregular triangle, where row r >= 1 has length 2^r and row sum is A103897(r), the sequence begins:
   2,  1;
   6,  5,  4,  3;
  14, 13, 12, 11, 10,  9,  8,  7;
  30, 29, 28, 27, 26, 25, 24, 23, 22, 21, 20, 19, 18, 17, 16, 15;
  ... (End)

Mathematica

(See A007931.)
A346306[rowmax_]:=Table[Range[2^(r+1)-2, 2^r-1, -1], {r, rowmax}]; A346306[6] (* Paolo Xausa, Mar 09 2023 *)

Prog

(Python)
from itertools import product
def comp(s): z, o = ord('0'), ord('1'); return s.translate({z:o, o:z})
def wgen(maxdigits):
    for digits in range(1, maxdigits+1):
        for b in product("01", repeat=digits):
            yield "".join(b)
def auptod(maxdigits):
    w = [None] + [wn for wn in wgen(maxdigits)]
    return [w.index(comp(w[n])) for n in range(1, 2**(maxdigits+1) - 1)]
print(auptod(6)) # Michael S. Branicky, Sep 03 2021

Crossrefs

Cf. A007931, A076478, A103897, A171757, A346303, A346304.

Sequence in context: A376674 A361198 A359806 * A021826 A331435 A159927

Adjacent sequences: A346303 A346304 A346305 * A346307 A346308 A346309

Keyword

nonn,tabf,base

Author

Clark Kimberling, Aug 16 2021

Status

approved