A272680 Smallest square that begins with n (in binary).

0, 1, 4, 25, 4, 81, 25, 121, 16, 9, 81, 361, 25, 441, 225, 121, 16, 1089, 36, 625, 81, 169, 361, 1521, 49, 25, 841, 441, 225, 3721, 121, 2025, 64, 529, 1089, 4489, 36, 2401, 1225, 625, 81, 5329, 169, 2809, 11449, 361, 5929, 1521, 6241, 49, 100, 6561, 841, 6889

Offset: 0

Author

N. J. A. Sloane, May 22 2016

Keywords

• nonn
• base
• easy

Examples

			a(10)=81, because 81 = 9^2 = 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, A272681.

Programs

Python

from gmpy2 import isqrt
def A272680(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(x)
            d *= 2
            nd *= 2 # Chai Wah Wu, May 22 2016

Extensions

More terms from Chai Wah Wu, May 22 2016