A371163 Numbers that remain unchanged when converted to their compressed fibbinary numbers.

0, 1, 2, 9, 10, 115544, 13568075, 13568077, 13568078, 13568083, 13568085, 13568086

Offset: 1

Author

Douglas Boffey, Mar 13 2024

Keywords

• base
• nonn
• more

Examples

			9 is a term since 9 = 8 + 1 = F(6) + F(2), where F(i) is the i-th Fibonacci number, is Fibbinary A003714(9) = 10001_2, but then all '01's are compressed to '1', leaving A048679(9) = 1001_2, which is 9 itself again.
		

Crossrefs

Fixed points of A048679 and A048680.

Cf. A000045, A003714.

Programs

Python

from itertools import count, islice
def A371163_gen(): # generator of terms
    c = 0
    for n in count(0):
        if not (n<<1)&n:
            if  int(bin(n)[2:].replace('01','1'),2) == c:
                yield c
            c += 1
A371163_list = list(islice(A371163_gen(),6)) # Chai Wah Wu, Mar 18 2024