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

Author

Clark Kimberling, Aug 16 2021

Keywords

• nonn
• tabf
• base

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

Examples

			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)
		

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

Crossrefs

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

Programs

Mathematica

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

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

Formula

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