A030690 -id:A030690 - cp's OEIS frontend

A030691 Cube root of A030690.

5, 16, 21, 55, 63, 154, 17, 40, 201, 10, 23, 113, 257, 27, 609, 295, 307, 148, 1535, 342, 164, 1692, 809, 1793, 397, 878, 90, 428, 944, 4482, 987, 1008, 1029, 4872, 107, 2349, 5154, 5247, 2478, 252, 552, 5609, 5697, 5785, 2726, 1284, 2806, 6131

Offset: 1

Patrick De Geest

Smallest m such that m^3 begins with n^2.

			a(4)=55 because 55^3=166375 begins with 4^2=16. - _Zak Seidov_, Oct 18 2011

Zak Seidov, Table of n, a(n) for n = 1..1000

s={}; Do[If[n==3, AppendTo[s,21], k=1; While[(ra=Range[Ceiling[(n^2*10^k)^(1/3)], Floor[((n^2+1)*10^k)^(1/3)]]) == {}, k++]; AppendTo[s, ra[[1]]]], {n,100}]; s (* Zak Seidov, Oct 18 2011 *)

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

Original entry on oeis.org

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

Zak Seidov, Mar 05 2008

Differs from A030691.

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

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

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

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

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

A138174 a(n) is the smallest cube that begins with n^2.

Original entry on oeis.org

1, 4096, 9261, 166375, 250047, 3652264, 4913, 64, 8120601, 1000, 12167, 1442897, 16974593, 19683, 225866529, 25672375, 28934443, 3241792, 3616805375, 40001688, 4410944, 4843965888, 529475129, 5764224257, 62570773, 676836152

Offset: 1

Zak Seidov, Mar 05 2008

Differs from A030690.

Cf. A030690, A030691, A018852, A018797, A077729, A077730, A138173.

a(n) = (A138173(n))^3.

Corrected by D. S. McNeil, Dec 12 2010

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A030691 Cube root of A030690.

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

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A138174 a(n) is the smallest cube that begins with n^2.

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