A272679 a(n)^2 is the smallest square whose binary expansion begins with the binary expansion of n.

0, 1, 2, 5, 2, 9, 5, 11, 4, 3, 9, 19, 5, 21, 15, 11, 4, 33, 6, 25, 9, 13, 19, 39, 7, 5, 29, 21, 15, 61, 11, 45, 8, 23, 33, 67, 6, 49, 35, 25, 9, 73, 13, 53, 107, 19, 77, 39, 79, 7, 10, 81, 29, 83, 59, 21, 15, 43, 61, 87, 11, 89, 63, 45, 8, 129, 23, 93, 33, 47

Offset: 0

Author

N. J. A. Sloane, May 22 2016

Keywords

• nonn
• base
• easy

Examples

			a(10)=9, because 9^2 = 81 = 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, A272680, A272681.

Programs

Python

from gmpy2 import isqrt
def A272679(n):
    if n == 0:
        return 0
    else:
        d, nd = 1, n
        while True:
            x = isqrt(nd-1)+1
            if x**2 < 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