A018005 -id:A018005 - cp's OEIS frontend

A061439 Largest number whose cube has n digits.

2, 4, 9, 21, 46, 99, 215, 464, 999, 2154, 4641, 9999, 21544, 46415, 99999, 215443, 464158, 999999, 2154434, 4641588, 9999999, 21544346, 46415888, 99999999, 215443469, 464158883, 999999999, 2154434690, 4641588833, 9999999999

Offset: 1

Amarnath Murthy, May 03 2001

a(n) + A181375(n) + A181377(n) + A181379(n) + A181381(n) + A181400(n) + A181402(n) + A181404(n) + A130130(n) = A002283(n).

			a(5) = 46 because 46^3 = 97336 has 5 digits, while 47^3 = 103823 has 6 digits.

a(n) is one more than the corresponding term of A018005. Cf. A061435.

Digits := 100:
A061439 := n->ceil(10^(n/3))-1:
seq (A061439(n), n=1..40);

t={}; i=0; Do[i=i+1; While[IntegerLength[i^3]<=n,i++]; AppendTo[t,i-1],{n,20}]; t (* Jayanta Basu, May 19 2013 *)

a(n) = ceiling(10^(n/3)) - 1. - Antonio G. Astudillo (afg_astudillo(AT)lycos.com), Mar 30 2003

More terms from Larry Reeves (larryr(AT)acm.org), May 16 2001

Typo in Maple program fixed by Martin Renner, Jan 31 2011

A373727 a(n) is the largest number that is the digit sum of an n-digit cube.

Original entry on oeis.org

8, 10, 18, 28, 28, 44, 46, 54, 63, 73, 80, 82, 98, 100, 109, 118, 125, 136, 144, 154, 154, 163, 172, 181, 190, 190, 199, 208, 217, 226, 235, 243, 253, 260, 262, 278

Offset: 1

Zhining Yang, Jun 15 2024

			a(7) = 46 because 46 is the largest digital sum encountered among all 7-digit cubes (attained at 3 cubes: 3869893, 7880599, 8998912).

Kevin Ryde, C Code

Cf. A018005, A061439.

Other powers: A371728, A373914, A374025, A373994.

C
```
/* See links. */
```

Table[Max@
  Map[Total@IntegerDigits[#^3] &,
   Range[Ceiling@CubeRoot[10^(n - 1)], CubeRoot[10^n - 1]]], {n, 15}]

from sympy import integer_nthroot
def A373727(n): return max(sum(int(d) for d in str(m**3)) for m in range(1+integer_nthroot(10**(n-1)-1,3)[0],1+integer_nthroot(10**n-1,3)[0])) # Chai Wah Wu, Jun 26 2024

A130080 Smallest number whose sixth power has n digits.

Original entry on oeis.org

1, 2, 3, 4, 5, 7, 10, 15, 22, 32, 47, 69, 100, 147, 216, 317, 465, 682, 1000, 1468, 2155, 3163, 4642, 6813, 10000, 14678, 21545, 31623, 46416, 68130, 100000, 146780, 215444, 316228, 464159, 681293, 1000000, 1467800, 2154435, 3162278, 4641589

Offset: 1

Klaus Brockhaus, May 07 2007

Powers of sixth root of 10 rounded up.

			6^6 = 46656 has five digits, 7^6 = 117649 has six digits, hence a(6) = 7.

Vincenzo Librandi, Table of n, a(n) for n = 1..1000

Cf. A011557 (powers of 10), A017936 (smallest number whose square has n digits), A018005 (smallest number whose cube has n digits), A018074 (smallest number whose fourth power has n digits), A018143 (smallest number whose fifth power has n digits), A130081 to A130084 (smallest number whose seventh ... tenth power has n digits).

[ Ceiling(Root(10^(n-1),6)): n in [1..41] ];

Table[(Ceiling[10^((n - 1)/6)]), {n, 1, 100}] (* Vincenzo Librandi, Sep 20 2013 *)

from sympy import integer_nthroot
def A130080(n):
    a, b = integer_nthroot(10**(n-1),6)
    return a+(not b) # Chai Wah Wu, Jun 19 2024

a(n) = ceiling(10^((n-1)/6)).

A130084 Smallest number whose tenth power has at least n digits.

Original entry on oeis.org

1, 2, 2, 2, 3, 4, 4, 6, 7, 8, 10, 13, 16, 20, 26, 32, 40, 51, 64, 80, 100, 126, 159, 200, 252, 317, 399, 502, 631, 795, 1000, 1259, 1585, 1996, 2512, 3163, 3982, 5012, 6310, 7944, 10000, 12590, 15849, 19953, 25119, 31623, 39811, 50119, 63096, 79433, 100000

Offset: 1

Klaus Brockhaus, May 07 2007

Powers of tenth root of 10 rounded up.

			3^10 = 59049 has five digits, 4^10 = 1048576 has seven digits, hence a(6) = a(7) = 4.

Vincenzo Librandi, Table of n, a(n) for n = 1..1000

Cf. A011279, A011557 (powers of 10), A017936 (smallest number whose square has n digits), A018005 (smallest number whose cube has n digits), A018074 (smallest number whose fourth power has n digits), A018143 (smallest number whose fifth power has n digits), A130080 to A130083 (smallest number whose sixth ... ninth power has n digits).

[Ceiling(Root(10^(n-1),10)): n in [1..51]];

Table[(Ceiling[10^((n - 1)/10)]), {n, 1, 60}] (* Vincenzo Librandi, Sep 20 2013 *)

from sympy import integer_nthroot
def A130084(n): return (lambda x:x[0]+(not x[1]))(integer_nthroot(10**(n-1),10)) # Chai Wah Wu, Jun 20 2024

a(n) = ceiling(10^((n-1)/10)).

A130083 Smallest number whose ninth power has at least n digits.

Original entry on oeis.org

1, 2, 2, 3, 3, 4, 5, 6, 8, 10, 13, 17, 22, 28, 36, 47, 60, 78, 100, 130, 167, 216, 279, 360, 465, 600, 775, 1000, 1292, 1669, 2155, 2783, 3594, 4642, 5995, 7743, 10000, 12916, 16682, 21545, 27826, 35939, 46416, 59949, 77427, 100000, 129155, 166811, 215444

Offset: 1

Klaus Brockhaus, May 07 2007

Powers of ninth root of 10 rounded up.

			2^9 = 512 has three digits, 3^9 = 19683 has five digits, hence a(4) = a(5) = 3.

Vincenzo Librandi, Table of n, a(n) for n = 1..1000

Cf. A011278, A011557 (powers of 10), A017936 (smallest number whose square has n digits), A018005 (smallest number whose cube has n digits), A018074 (smallest number whose fourth power has n digits), A018143 (smallest number whose fifth power has n digits), A130080 to A130084 (smallest number whose sixth ... tenth power has n digits).

[ Ceiling(Root(10^(n-1),9)): n in [1..49] ];

Table[(Ceiling[10^((n - 1)/9)]), {n, 1, 60}] (* Vincenzo Librandi, Sep 21 2013 *)

from sympy import integer_nthroot
def A130083(n): return (lambda x:x[0]+(not x[1]))(integer_nthroot(10**(n-1),9)) # Chai Wah Wu, Jun 20 2024

a(n) = ceiling(10^((n-1)/9)).

A130081 Smallest number whose seventh power has at least n digits.

Original entry on oeis.org

1, 2, 2, 3, 4, 6, 8, 10, 14, 20, 27, 38, 52, 72, 100, 139, 194, 269, 373, 518, 720, 1000, 1390, 1931, 2683, 3728, 5180, 7197, 10000, 13895, 19307, 26827, 37276, 51795, 71969, 100000, 138950, 193070, 268270, 372760, 517948, 719686, 1000000, 1389496

Offset: 1

Klaus Brockhaus, May 07 2007

Powers of seventh root of 10 rounded up.

			1^7 = 1 has 1 digit, 2^7 = 128 has three digits, hence a(2) = a(3) = 2.

Vincenzo Librandi, Table of n, a(n) for n = 1..1000

Cf. A011276, A011557 (powers of 10), A017936 (smallest number whose square has n digits), A018005 (smallest number whose cube has n digits), A018074 (smallest number whose fourth power has n digits), A018143 (smallest number whose fifth power has n digits), A130080 to A130084 (smallest number whose sixth ... tenth power has n digits).

[Ceiling(Root(10^(n-1),7)): n in [1..44]];

Table[(Ceiling[10^((n - 1)/7)]), {n, 1, 60}] (* Vincenzo Librandi, Sep 20 2013 *)

from sympy import integer_nthroot
def A130081(n): return (lambda x:x[0]+(not x[1]))(integer_nthroot(10**(n-1),7)) # Chai Wah Wu, Jun 20 2024

a(n) = ceiling(10^((n-1)/7)).

A130082 Smallest number whose eighth power has at least n digits.

Original entry on oeis.org

1, 2, 2, 3, 4, 5, 6, 8, 10, 14, 18, 24, 32, 43, 57, 75, 100, 134, 178, 238, 317, 422, 563, 750, 1000, 1334, 1779, 2372, 3163, 4217, 5624, 7499, 10000, 13336, 17783, 23714, 31623, 42170, 56235, 74990, 100000, 133353, 177828, 237138, 316228, 421697

Offset: 1

Klaus Brockhaus, May 07 2007

Powers of eighth root of 10 rounded up.

			9^8 = 43046721 has eight digits, 10^8 = 100000000 has nine digits, hence a(9) = 10.

Vincenzo Librandi, Table of n, a(n) for n = 1..1000

Cf. A011277, A011557 (powers of 10), A017936 (smallest number whose square has n digits), A018005 (smallest number whose cube has n digits), A018074 (smallest number whose fourth power has n digits), A018143 (smallest number whose fifth power has n digits), A130080 to A130084 (smallest number whose sixth ... tenth power has n digits).

[ Ceiling(Root(10^(n-1),8)): n in [1..46] ];

Table[(Ceiling[10^((n - 1)/8)]), {n, 1, 60}] (* Vincenzo Librandi, Sep 20 2013 *)

from sympy import integer_nthroot
def A130082(n): return (lambda x:x[0]+(not x[1]))(integer_nthroot(10**(n-1),8)) # Chai Wah Wu, Jun 20 2024

a(n) = ceiling(10^((n-1)/8)).

cp's OEIS Frontend

A061439 Largest number whose cube has n digits.

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A373727 a(n) is the largest number that is the digit sum of an n-digit cube.

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A130080 Smallest number whose sixth power has n digits.

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A130084 Smallest number whose tenth power has at least n digits.

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A130083 Smallest number whose ninth power has at least n digits.

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A130081 Smallest number whose seventh power has at least n digits.

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A130082 Smallest number whose eighth power has at least n digits.

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