A017981 -id:A017981 - cp's OEIS frontend

A018005 Smallest number whose cube has n digits.

1, 3, 5, 10, 22, 47, 100, 216, 465, 1000, 2155, 4642, 10000, 21545, 46416, 100000, 215444, 464159, 1000000, 2154435, 4641589, 10000000, 21544347, 46415889, 100000000, 215443470, 464158884, 1000000000, 2154434691, 4641588834

Offset: 1

N. J. A. Sloane

With offset 0, ((cube root of 10) to the power n) rounded up.
From Carmine Suriano, Mar 14 2020: (Start)
The terms corresponding to n = (20,21); (38,39); (41,42); (56,57); (59,60); (77,78); (80,81) ... are such that the square of first term starts with the digits of second term, and the square of second term starts with the digits of the first. For example, a(38)^2 = 2154434690032^2 = 4641588833613.... and a(39)^2 = 4641588833613^2 = 2154434690032...
 (End)

			a(5) = 22, 22^3 = 10648 has 5 digits, while 21^3 = 9261 has 4 digits.

Vincenzo Librandi, Table of n, a(n) for n = 1..200

Cf. A061434, A061439, and powers of cube root of k ceiling up: A017981 (k=2), A017984 (k=3), A017987 (k=4), A017990 (k=5), A017993 (k=6), A017996 (k=7), A018002 (k=9), this sequence (k=10), A018008 (k=11), A018011 (k=12), A018014 (k=13), A018017 (k=14), A018020 (k=15), A018023 (k=16), A018026 (k=17), A018029 (k=18), A018032 (k=19), A018035 (k=20), A018038 (k=21), A018041 (k=22), A018044 (k=23), A018047 (k=24).

[Ceiling(10^(n/3)): n in [0..40]]; // Vincenzo Librandi, Jan 09 2014

Table[Ceiling[10^(n/3)], {n, 0, 40}] (* Vincenzo Librandi, Jan 09 2014 *)

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

A017979 Powers of cube root of 2 rounded down.

Original entry on oeis.org

1, 1, 1, 2, 2, 3, 4, 5, 6, 8, 10, 12, 16, 20, 25, 32, 40, 50, 64, 80, 101, 128, 161, 203, 256, 322, 406, 512, 645, 812, 1024, 1290, 1625, 2048, 2580, 3250, 4096, 5160, 6501, 8192, 10321, 13003, 16384, 20642, 26007, 32768, 41285, 52015, 65536, 82570, 104031

Offset: 0

N. J. A. Sloane

nonn

Rounding has no effect when n is a multiple of 3, because then obviously (2^(1/3))^n = 2^(n/3). - Alonso del Arte, Jan 04 2014

			a(2) = 1 because the cube root of 2 squared is 1.5874...
a(3) = 2 because the cube root of 2 cubed is 2 exactly.
a(4) = 2 because the cube root of 2 to the fourth power is 2.519842...

Vincenzo Librandi, Table of n, a(n) for n = 0..200

Cf. A017981, A002580.

Sequences of the type: Powers of cube root of (k) rounded down: this sequence (k=2), A017982 (k=3), A017985 (k=4), A017988 (k=5), A017991 (k=6), A017994 (k=7), A018000 (k=9), A018003 (k=10), A018006 (k=11), A018009 (k=12), A018012 (k=13), A018015 (k=14), A018018 (k=15), A018021 (k=16), A018024 (k=17), A018027 (k=18), A018030 (k=19), A018033 (k=20), A018036 (k=21), A018039 (k=22), A018042 (k=23), A018045 (k=24).

[Floor(2^(n/3)): n in [0..50]]; // Vincenzo Librandi, Jan 06 2014

Table[Floor[(2^(1/3))^n], {n, 0, 49}] (* Alonso del Arte, Jan 04 2014 *)

from sympy import integer_nthroot
def A017979(n): return integer_nthroot(1<Chai Wah Wu, Jun 18 2024

a(44)-a(50) from Alex Ratushnyak, Jan 04 2014

A018026 Powers of cube root of 17 rounded up.

Original entry on oeis.org

1, 3, 7, 17, 44, 113, 289, 744, 1911, 4913, 12633, 32483, 83521, 214757, 552199, 1419857, 3650853, 9387369, 24137569, 62064487, 159585273, 410338673, 1055096276, 2712949631, 6975757441, 17936636689, 46120143717, 118587876497, 304922823712

Offset: 0

N. J. A. Sloane

nonn

Vincenzo Librandi, Table of n, a(n) for n = 0..200

Cf. A010589, A018024, A018025, and powers of cube root of k ceiling up: A017981 (k=2), A017984 (k=3), A017987 (k=4), A017990 (k=5), A017993 (k=6), A017996 (k=7), A018002 (k=9), A018005 (k=10), A018008 (k=11), A018011 (k=12), A018014 (k=13), A018017 (k=14), A018020 (k=15), A018023 (k=16), this sequence (k=17), A018029 (k=18), A018032 (k=19), A018035 (k=20), A018038 (k=21), A018041 (k=22), A018044 (k=23), A018047 (k=24).

[Ceiling(17^(n/3)): n in [0..40]]; // Vincenzo Librandi, Jan 10 2014

Digits:= 1000:
a:= n-> ceil(17^(n/3)):
seq(a(n), n=0..30);  # Alois P. Heinz, Nov 23 2013

Table[Ceiling[17^(n/3)], {n, 0, 40}] (* Vincenzo Librandi, Jan 10 2014 *)

a(n) = if (n % 3, ceil((17^(1/3))^n), 17^(n/3)); \\ Michel Marcus, Nov 23 2013

A017984 Powers of cube root of 3 rounded up.

Original entry on oeis.org

1, 2, 3, 3, 5, 7, 9, 13, 19, 27, 39, 57, 81, 117, 169, 243, 351, 506, 729, 1052, 1517, 2187, 3155, 4550, 6561, 9463, 13648, 19683, 28388, 40943, 59049, 85164, 122827, 177147, 255491, 368481, 531441, 766471, 1105442, 1594323, 2299412, 3316326, 4782969, 6898235

Offset: 0

N. J. A. Sloane

nonn

Smallest integer such that a(n)^k-k^n is nonnegative for all nonnegative integers k. - Henry Bottomley, May 16 2005

Vincenzo Librandi, Table of n, a(n) for n = 0..200

Cf. A107586 and powers of cube root of k ceiling up: A017981 (k=2), this sequence (k=3), A017987 (k=4), A017990 (k=5), A017993 (k=6), A017996 (k=7), A018002 (k=9), A018005 (k=10), A018008 (k=11), A018011 (k=12), A018014 (k=13), A018017 (k=14), A018020 (k=15), A018023 (k=16), A018026 (k=17), A018029 (k=18), A018032 (k=19), A018035 (k=20), A018038 (k=21), A018041 (k=22), A018044 (k=23), A018047 (k=24).

[Ceiling(3^(n/3)): n in [0..50]]; // Vincenzo Librandi, Jan 09 2014

Table[Ceiling[3^(n/3)], {n, 0, 50}] (* Vincenzo Librandi, Jan 09 2014 *)

a(n)=ceil(3^(n/3)) \\ Charles R Greathouse IV, Jan 09 2014

More terms from Vincenzo Librandi, Jan 09 2014

A017987 Powers of cube root of 4 rounded up.

Original entry on oeis.org

1, 2, 3, 4, 7, 11, 16, 26, 41, 64, 102, 162, 256, 407, 646, 1024, 1626, 2581, 4096, 6502, 10322, 16384, 26008, 41286, 65536, 104032, 165141, 262144, 416128, 660562, 1048576, 1664511, 2642246, 4194304, 6658043, 10568984, 16777216, 26632171, 42275936, 67108864

Offset: 0

N. J. A. Sloane

nonn

Vincenzo Librandi, Table of n, a(n) for n = 0..200
J. Peebles, Cap Set Bounds and Matrix Multiplication, Math 197: Senior Thesis, Harvey Mudd College, 2013.

Cf. powers of cube root of k ceiling up: A017981 (k=2), A017984 (k=3), this sequence (k=4), A017990 (k=5), A017993 (k=6), A017996 (k=7), A018002 (k=9), A018005 (k=10), A018008 (k=11), A018011 (k=12), A018014 (k=13), A018017 (k=14), A018020 (k=15), A018023 (k=16), A018026 (k=17), A018029 (k=18), A018032 (k=19), A018035 (k=20), A018038 (k=21), A018041 (k=22), A018044 (k=23), A018047 (k=24).

[Ceiling(4^(n/3)): n in [0..50]]; // Vincenzo Librandi, Jan 09 2014

Ceiling[Surd[4,3]^Range[0,40]] (* Harvey P. Dale, May 15 2013 *)
Table[Ceiling[4^(n/3)], {n, 0, 40}] (* Vincenzo Librandi, Jan 09 2014 *)

More terms from Vincenzo Librandi, Jan 09 2014

A017990 Powers of cube root of 5 rounded up.

Original entry on oeis.org

1, 2, 3, 5, 9, 15, 25, 43, 74, 125, 214, 366, 625, 1069, 1828, 3125, 5344, 9138, 15625, 26719, 45688, 78125, 133592, 228439, 390625, 667960, 1142195, 1953125, 3339797, 5710973, 9765625, 16698984, 28554861, 48828125, 83494920, 142774304, 244140625

Offset: 0

N. J. A. Sloane

nonn

Vincenzo Librandi, Table of n, a(n) for n = 0..200

Cf. powers of cube root of k ceiling up: A017981 (k=2), A017984 (k=3), A017987 (k=4), this sequence (k=5), A017993 (k=6), A017996 (k=7), A018002 (k=9), A018005 (k=10), A018008 (k=11), A018011 (k=12), A018014 (k=13), A018017 (k=14), A018020 (k=15), A018023 (k=16), A018026 (k=17), A018029 (k=18), A018032 (k=19), A018035 (k=20), A018038 (k=21), A018041 (k=22), A018044 (k=23), A018047 (k=24).

[Ceiling(5^(n/3)): n in [0..50]]; // Vincenzo Librandi, Jan 09 2014

Table[Ceiling[5^(n/3)], {n, 0, 40}] (* Vincenzo Librandi, Jan 09 2014 *)

More terms from Vincenzo Librandi, Jan 09 2014

A017993 Powers of cube root of 6 rounded up.

Original entry on oeis.org

1, 2, 4, 6, 11, 20, 36, 66, 119, 216, 393, 714, 1296, 2355, 4280, 7776, 14130, 25676, 46656, 84780, 154055, 279936, 508678, 924329, 1679616, 3052065, 5545970, 10077696, 18312389, 33275820, 60466176, 109874334, 199654915, 362797056, 659246002

Offset: 0

N. J. A. Sloane

nonn

Vincenzo Librandi, Table of n, a(n) for n = 0..200

Cf. powers of cube root of k ceiling up: A017981 (k=2), A017984 (k=3), A017987 (k=4), A017990 (k=5), this sequence (k=6), A017996 (k=7), A018002 (k=9), A018005 (k=10), A018008 (k=11), A018011 (k=12), A018014 (k=13), A018017 (k=14), A018020 (k=15), A018023 (k=16), A018026 (k=17), A018029 (k=18), A018032 (k=19), A018035 (k=20), A018038 (k=21), A018041 (k=22), A018044 (k=23), A018047 (k=24).

[Ceiling(6^(n/3)): n in [0..50]]; // Vincenzo Librandi, Jan 09 2014

Table[Ceiling[6^(n/3)], {n, 0, 40}] (* Vincenzo Librandi, Jan 09 2014 *)

More terms from Vincenzo Librandi, Jan 09 2014

A017996 Powers of cube root of 7 rounded up.

Original entry on oeis.org

1, 2, 4, 7, 14, 26, 49, 94, 180, 343, 657, 1256, 2401, 4593, 8786, 16807, 32151, 61502, 117649, 225055, 430514, 823543, 1575382, 3013596, 5764801, 11027668, 21095170, 40353607, 77193674, 147666185, 282475249, 540355713, 1033663292, 1977326743, 3782489986

Offset: 0

N. J. A. Sloane

nonn

Vincenzo Librandi, Table of n, a(n) for n = 0..200

Cf. powers of cube root of k ceiling up: A017981 (k=2), A017984 (k=3), A017987 (k=4), A017990 (k=5), A017993 (k=6), this sequence (k=7), A018002 (k=9), A018005 (k=10), A018008 (k=11), A018011 (k=12), A018014 (k=13), A018017 (k=14), A018020 (k=15), A018023 (k=16), A018026 (k=17), A018029 (k=18), A018032 (k=19), A018035 (k=20), A018038 (k=21), A018041 (k=22), A018044 (k=23), A018047 (k=24).

[Ceiling(7^(n/3)): n in [0..50]]; // Vincenzo Librandi, Jan 09 2014

Table[Ceiling[7^(n/3)], {n, 0, 40}] (* Vincenzo Librandi, Jan 09 2014 *)

More terms from Vincenzo Librandi, Jan 09 2014

A018002 Powers of cube root of 9 rounded up.

Original entry on oeis.org

1, 3, 5, 9, 19, 39, 81, 169, 351, 729, 1517, 3155, 6561, 13648, 28388, 59049, 122827, 255491, 531441, 1105442, 2299412, 4782969, 9948977, 20694705, 43046721, 89540788, 186252345, 387420489, 805867092, 1676271102, 3486784401, 7252803827, 15086439913, 31381059609

Offset: 0

N. J. A. Sloane

nonn

Vincenzo Librandi, Table of n, a(n) for n = 0..200

Cf. powers of cube root of k ceiling up: A017981 (k=2), A017984 (k=3), A017987 (k=4), A017990 (k=5), A017993 (k=6), A017996 (k=7), this sequence (k=9), A018005 (k=10), A018008 (k=11), A018011 (k=12), A018014 (k=13), A018017 (k=14), A018020 (k=15), A018023 (k=16), A018026 (k=17), A018029 (k=18), A018032 (k=19), A018035 (k=20), A018038 (k=21), A018041 (k=22), A018044 (k=23), A018047 (k=24).

[Ceiling(9^(n/3)): n in [0..50]]; // Vincenzo Librandi, Jan 09 2014

Table[Ceiling[9^(n/3)], {n, 0, 40}] (* Vincenzo Librandi, Jan 09 2014 *)

More terms from Vincenzo Librandi, Jan 09 2014

A018011 Powers of cube root of 12 rounded up.

Original entry on oeis.org

1, 3, 6, 12, 28, 63, 144, 330, 755, 1728, 3957, 9058, 20736, 47474, 108688, 248832, 569684, 1304249, 2985984, 6836197, 15650984, 35831808, 82034362, 187811805, 429981696, 984412343, 2253741659, 5159780352, 11812948115, 27044899908, 61917364224

Offset: 0

N. J. A. Sloane

nonn

Vincenzo Librandi, Table of n, a(n) for n = 0..200

Cf. powers of cube root of k ceiling up: A017981 (k=2), A017984 (k=3), A017987 (k=4), A017990 (k=5), A017993 (k=6), A017996 (k=7), A018002 (k=9), A018005 (k=10), A018008 (k=11), this sequence (k=12), A018014 (k=13), A018017 (k=14), A018020 (k=15), A018023 (k=16), A018026 (k=17), A018029 (k=18), A018032 (k=19), A018035 (k=20), A018038 (k=21), A018041 (k=22), A018044 (k=23), A018047 (k=24).

[Ceiling(12^(n/3)): n in [0..40]]; // Vincenzo Librandi, Jan 09 2014

Table[Ceiling[12^(n/3)], {n, 0, 40}] (* Vincenzo Librandi, Jan 09 2014 *)

More terms from Vincenzo Librandi, Jan 09 2014

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A018005 Smallest number whose cube has n digits.

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A017979 Powers of cube root of 2 rounded down.

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A018026 Powers of cube root of 17 rounded up.

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A017984 Powers of cube root of 3 rounded up.

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A017987 Powers of cube root of 4 rounded up.

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A017990 Powers of cube root of 5 rounded up.

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A017993 Powers of cube root of 6 rounded up.

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A017996 Powers of cube root of 7 rounded up.