A377169 Nonnegative integers containing isolated ones in their binary representation.

1, 2, 4, 5, 8, 9, 10, 11, 13, 16, 17, 18, 19, 20, 21, 22, 23, 25, 26, 29, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 49, 50, 52, 53, 57, 58, 61, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87

Offset

1,2

Comments

A 1 is isolated if it's not adjacent to another 1.

Links

Paolo Xausa, Table of n, a(n) for n = 1..10000

Example

19 is a term because 19 = 10011_2 contains one isolated 1.
74 is a term because all ones in 74 = 1001010_2 are isolated.

Mathematica

Select[Range[150], MemberQ[Split[IntegerDigits[#, 2]], {1}] &]

Prog

(Python)
from sympy import Matrix
def A377169(n):
    def f(x):
        s = bin(x)[-1:1:-1]
        t = '0'+s+'0'
        return n-1+sum((Matrix([[2, -1, 1], [1, 0, 0], [0, 1, 0]])**i*Matrix([1, 1, 0]))[0] for i in range(len(s)) if s[i]=='1' and not '010' in '0'+t[i+2:])+('010' not in t)
    m, k = n, f(n)
    while m != k: m, k = k, f(k)
    return m # Chai Wah Wu, Jun 10 2026

Crossrefs

Complement of A144795.

Cf. A004752, A007088, A377167.

Sequence in context: A130048 A189633 A032891 * A384879 A035262 A010440

Adjacent sequences: A377166 A377167 A377168 * A377170 A377171 A377172

Keyword

nonn,base,easy

Author

Paolo Xausa, Oct 18 2024

Status

approved