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
Links
- Chai Wah Wu, Table of n, a(n) for n = 1..10000
Programs
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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
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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).
Comments