A077730 -id:A077730 - cp's OEIS frontend

A077729 Smallest square beginning with n copies of n.

1, 225, 3330625, 44448889, 55555432804, 6666662032144, 77777777127241, 8888888859057216, 99999999989350756, 101010101010101010103146096508501770025, 1111111111111111111111185920458269940592889, 121212121212121212121212460158453802091945103889

Offset: 1

Amarnath Murthy, Nov 19 2002

From a(1) up to a(12), except for n = 7, these smallest squares begin with exactly n copies of n, but a(7) begins with 8 copies of 7. What is the smallest square beginning with exactly 7 copies of 7? - Bernard Schott, Jan 29 2022

27888667^2 = 777777747036889 begins with exactly 7 copies of 7. - Michel Marcus, Jan 30 2022

Cf. A077730.

Corrected and extended by Sascha Kurz, Jan 04 2003

a(11)-a(12) from Bernard Schott, Jan 29 2022

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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A077729 Smallest square beginning with n copies of n.

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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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