A383667 Binary words beginning with 1 in which no binary digit occurs only once.

11, 111, 1001, 1010, 1100, 1111, 10001, 10010, 10011, 10100, 10101, 10110, 11000, 11001, 11010, 11100, 11111, 100001, 100010, 100011, 100100, 100101, 100110, 100111, 101000, 101001, 101010, 101011, 101100, 101101, 101110, 110000, 110001, 110010, 110011

Offset

1,1

Links

Table of n, a(n) for n=1..35.

Mathematica

s = Select[Range[200], DigitCount[#, 2, 0] != 1 && DigitCount[#, 2, 1] != 1 &]
Map[First, RealDigits[s, 2]]; Map[FromDigits, m]

Prog

(Python)
def A383667(n):
    def f(x):
        if x<=1: return n+x
        l, s = x.bit_length(), bin(x)[2:]
        if (m:=s.count('0'))>0: return n+s.index('0')-(m>1)+(l*(l-1)>>1)
        return n-1+(l*(l+1)>>1)
    m, k = n, f(n)
    while m != k: m, k = k, f(k)
    return int(bin(m)[2:]) # Chai Wah Wu, May 21 2025

Crossrefs

Cf. A158581, A383666.

Sequence in context: A143573 A248039 A244204 * A058947 A282912 A284025

Adjacent sequences: A383664 A383665 A383666 * A383668 A383669 A383670

Keyword

nonn,base

Author

Clark Kimberling, May 07 2025

Status

approved