A344346 Numbers k which have an odd number of trailing zeros in their binary reflected Gray code A014550(k).

3, 4, 11, 12, 15, 16, 19, 20, 27, 28, 35, 36, 43, 44, 47, 48, 51, 52, 59, 60, 63, 64, 67, 68, 75, 76, 79, 80, 83, 84, 91, 92, 99, 100, 107, 108, 111, 112, 115, 116, 123, 124, 131, 132, 139, 140, 143, 144, 147, 148, 155, 156, 163, 164, 171, 172, 175, 176, 179, 180

Offset

1,1

Comments

Numbers k such that A050605(k-1) is odd.

Numbers k such that A136480(k) is even.

The asymptotic density of this sequence is 1/3.

Links

Amiram Eldar, Table of n, a(n) for n = 1..10000

Eric Weisstein's World of Mathematics, Gray Code.

Wikipedia, Gray code.

Index entries for 2-automatic sequences.

Formula

a(n) = A081706(n) + 1. - Hugo Pfoertner, May 16 2021

Example

3 is a term since its Gray code, 10, has 1 trailing zero, and 1 is odd.
15 is a term since its Gray code, 1000, has 3 trailing zeros, and 3 is odd.

Mathematica

Select[Range[180], OddQ @ IntegerExponent[# * (# + 1)/2, 2] &]

Prog

(Python)
def A344346(n):
    def f(x):
        c, s = (n+1>>1)+x, bin(x)[2:]
        l = len(s)
        for i in range(l&1^1, l, 2):
            c -= int(s[i])+int('0'+s[:i], 2)
        return c
    m, k = n, f(n)
    while m != k: m, k = k, f(k)
    return (m<<2)-(n&1) # Chai Wah Wu, Jan 29 2025

Crossrefs

Cf. A014550, A050605, A081706, A136480.

Similar sequences: A001950 (Zeckendorf), A036554 (binary), A145204 (ternary), A217319 (quaternary), A232745 (factorial), A342050 (primorial).

Sequence in context: A339578 A244005 A228236 * A047457 A226632 A098377

Adjacent sequences: A344343 A344344 A344345 * A344347 A344348 A344349

Keyword

nonn,base,easy

Author

Amiram Eldar, May 15 2021

Status

approved