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

0,3

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

Example

a(10)=9, because 9^2 = 81 = 1010001_2 begins with 1010 = 10_2.

Prog

(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

Crossrefs

Cf. A007088, A018851, A018796, A272680, A272681.

Sequence in context: A347378 A336853 A273580 * A119764 A178310 A210697

Adjacent sequences: A272676 A272677 A272678 * A272680 A272681 A272682

Keyword

nonn,base,easy

Author

N. J. A. Sloane, May 22 2016

Extensions

More terms from Chai Wah Wu, May 22 2016

Status

approved