A207063 a(n) is the smallest number larger than a(n-1) with mutual Hamming distance 2 and a(1)=0.

0, 3, 5, 6, 10, 12, 15, 23, 27, 29, 30, 46, 54, 58, 60, 63, 95, 111, 119, 123, 125, 126, 190, 222, 238, 246, 250, 252, 255, 383, 447, 479, 495, 503, 507, 509, 510, 766, 894, 958, 990, 1006, 1014, 1018, 1020, 1023, 1535, 1791, 1919, 1983, 2015, 2031, 2039, 2043

Offset: 1

Author

Alois P. Heinz, Feb 14 2012

Keywords

• nonn
• base

Comments

The binary expansion of a(n) has an even number of 1's. So this is a subsequence of A001969. The odd analog is A206853.

This sequence has 4*k+1 = A016813(k) numbers with exactly 2*k 1's and no number with more than two 0's in their binary expansion.

Examples

			| n | a(n) | A007088(a(n))| A000120(a(n))|
+---+------+--------------+--------------+
| 1 |   0  |         0    |       0      |
| 2 |   3  |        11    |       2      |
| 3 |   5  |       101    |       2      |
| 4 |   6  |       110    |       2      |
| 5 |  10  |      1010    |       2      |
| 6 |  12  |      1100    |       2      |
| 7 |  15  |      1111    |       4      |
| 8 |  23  |     10111    |       4      |
		

Links

• Alois P. Heinz, Table of n, a(n) for n = 1..20000

Crossrefs

Cf. A182187 (next with Hamming distance 2), A206853 (iterate from 1).

Cf. A000120, A001969, A007088, A016813.

Programs

Maple

g:= proc(n) option remember; local l; l:= g(n-1);
      `if`(nops(l)=1, [l[1]+1, l[1]-1], `if`(nops(l)=2,
      `if`(l[2]<>0, [l[1], l[2]-1], [l[1]+1, 0, l[1]-1]),
      `if`(l[3]<>1, [l[1], l[2], l[3]-1], [l[1]])))
    end: g(1):= [2, 0, 1]:
a:= n-> (l-> 2^l[1]-1 -add(2^l[i], i=2..nops(l)))(g(n)):
seq(a(n), n=1..300);

Python

def aupton(terms):
    alst = [0]
    for n in range(2, terms+1):
        an = alst[-1] + 1
        while bin(an^alst[-1]).count('1') != 2:  an += 1
        alst.append(an)
    return alst
print(aupton(54)) # Michael S. Branicky, Jul 07 2021