A272681 Smallest binary square that begins with the binary expansion of n.

0, 1, 100, 11001, 100, 1010001, 11001, 1111001, 10000, 1001, 1010001, 101101001, 11001, 110111001, 11100001, 1111001, 10000, 10001000001, 100100, 1001110001, 1010001, 10101001, 101101001, 10111110001, 110001, 11001, 1101001001, 110111001, 11100001, 111010001001

Offset: 0

Author

N. J. A. Sloane, May 22 2016

Keywords

• nonn
• base
• easy

Examples

			a(10)=1010001 = 81_10, because 1010001_2 begins with 1010 = 10_2.
		

References

• Allan C. Wechsler, posting to math-fun mailing list May 22 2016.

Links

• Chai Wah Wu, Table of n, a(n) for n = 0..10000

Crossrefs

Cf. A007088, A018851, A018796, A272679, A272680.

Programs

Python

from gmpy2 import isqrt
def A272681(n):
    if n == 0:
        return 0
    else:
        d, nd = 1, n
        while True:
            x = (isqrt(nd-1)+1)**2
            if x < nd+d:
                return int(bin(x)[2:])
            d *= 2
            nd *= 2 # Chai Wah Wu, May 22 2016

Extensions

More terms from Chai Wah Wu, May 22 2016