A138173 a(n) is the smallest m such that m^3 begins with n^2.

1, 16, 21, 55, 63, 154, 17, 4, 201, 10, 23, 113, 257, 27, 609, 295, 307, 148, 1535, 342, 164, 1692, 809, 1793, 397, 878, 9, 428, 944, 4482, 987, 1008, 1029, 4872, 107, 2349, 5154, 5247, 2478, 252, 552, 5609, 5697, 5785, 2726, 1284, 2806, 6131, 2885

Offset: 1

Author

Zak Seidov, Mar 05 2008

Keywords

• nonn
• base

Comments

Differs from A030691.

Links

• Chai Wah Wu, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A030690, A030691, A018852, A018797, A077729, A077730, A138174.

Programs

Python

from gmpy2 import iroot
def A138173(n):
    d, nd = 1, n**2
    while True:
        x = iroot(nd-1,3)[0]+1
        if x**3 < nd+d:
            return int(x)
        d *= 10
        nd *= 10 # Chai Wah Wu, May 24 2016

Sage

A138173 = lambda n: next(m for m in IntegerRange(1, infinity) if str(m**3).startswith(str(n**2)))
# D. S. McNeil, Dec 12 2010

Formula

a(n) = (A138174(n))^(1/3).