A018006 -id:A018006 - cp's OEIS frontend

A017979 Powers of cube root of 2 rounded down.

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

A018007 Powers of cube root of 11 rounded to nearest integer.

Original entry on oeis.org

1, 2, 5, 11, 24, 54, 121, 269, 598, 1331, 2960, 6583, 14641, 32561, 72416, 161051, 358174, 796572, 1771561, 3939916, 8762296, 19487171, 43339080, 96385252, 214358881, 476729884, 1060237770, 2357947691, 5244028719, 11662615466, 25937424601, 57684315913

Offset: 0

N. J. A. Sloane

nonn

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

Cf. A018006, and powers of cube root of k rounded up: A017980 (k=2), A017983 (k=3), A017986 (k=4), A017989 (k=5), A017992 (k=6), A017995 (k=7), A018001 (k=9), A018004 (k=10), this sequence (k=11), A018010 (k=12), A018013 (k=13), A018016 (k=14), A018019 (k=15), A018022 (k=16), A018025 (k=17), A018028 (k=18), A018031 (k=19), A018034 (k=20), A018037 (k=21), A018040 (k=22), A018043 (k=23), A018046 (k=24).

[Round(11^(n/3)): n in [0..50]]; // Vincenzo Librandi, Jan 08 2014

A018007:=n->round(11^(n/3)); seq(A018007(n), n=0..50); # Wesley Ivan Hurt, Dec 21 2013

Table[Round[11^(n/3)], {n, 0, 50}] (* Wesley Ivan Hurt, Dec 21 2013 *)

a(n) = round( 11^(n/3) ). - Wesley Ivan Hurt, Dec 21 2013

More terms from Vincenzo Librandi, Jan 08 2014

A018024 Powers of cube root of 17 rounded down.

Original entry on oeis.org

1, 2, 6, 17, 43, 112, 289, 743, 1910, 4913, 12632, 32482, 83521, 214756, 552198, 1419857, 3650852, 9387368, 24137569, 62064486, 159585272, 410338673, 1055096275, 2712949630, 6975757441, 17936636688, 46120143716, 118587876497, 304922823711, 784042443182

Offset: 0

N. J. A. Sloane

nonn

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

Cf. A010589, A018025, A018026, and powers of cube root of k rounded down: A017979 (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), this sequence (k=17), A018027 (k=18), A018030 (k=19), A018033 (k=20), A018036 (k=21), A018039 (k=22), A018042 (k=23), A018045 (k=24).

[Floor(17^(n/3)): n in [0..40]]; // Vincenzo Librandi, Jan 06 2014

Table[Floor[17^(n/3)], {n, 0, 40}]  (* Vincenzo Librandi, Jan 06 2014 *)

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

More terms from Michel Marcus, Nov 23 2013

A017982 Powers of cube root of 3 rounded down.

Original entry on oeis.org

1, 1, 2, 3, 4, 6, 9, 12, 18, 27, 38, 56, 81, 116, 168, 243, 350, 505, 729, 1051, 1516, 2187, 3154, 4549, 6561, 9462, 13647, 19683, 28387, 40942, 59049, 85163, 122826, 177147, 255490, 368480, 531441, 766470, 1105441, 1594323, 2299411, 3316325, 4782969, 6898234

Offset: 0

N. J. A. Sloane

nonn

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

Cf. sequences of the type: Powers of cube root of (k) rounded down A017979 (k=2), this sequence (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(3^(n/3)): n in [0..50]]; // Vincenzo Librandi, Jan 06 2014

Table[Floor[3^(n/3)], {n, 0, 50}] (* Vincenzo Librandi, Jan 06 2014 *)

More terms from Vincenzo Librandi, Jan 06 2014

A017985 Powers of cube root of 4 rounded down.

Original entry on oeis.org

1, 1, 2, 4, 6, 10, 16, 25, 40, 64, 101, 161, 256, 406, 645, 1024, 1625, 2580, 4096, 6501, 10321, 16384, 26007, 41285, 65536, 104031, 165140, 262144, 416127, 660561, 1048576, 1664510, 2642245, 4194304, 6658042, 10568983, 16777216, 26632170, 42275935, 67108864

Offset: 0

N. J. A. Sloane

nonn

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

Cf. sequences of the type: Powers of cube root of (k) rounded down A017979 (k=2), A017982 (k=3), this sequence (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(4^(n/3)): n in [0..50]]; // Vincenzo Librandi, Jan 06 2014

Table[Floor[4^(n/3)], {n, 0, 40}] (* Vincenzo Librandi, Jan 06 2014 *)

a(n) = floor(4^(n/3)). - Wesley Ivan Hurt, Sep 04 2022

More terms from Vincenzo Librandi, Jan 06 2014

A017988 Powers of cube root of 5 rounded down.

Original entry on oeis.org

1, 1, 2, 5, 8, 14, 25, 42, 73, 125, 213, 365, 625, 1068, 1827, 3125, 5343, 9137, 15625, 26718, 45687, 78125, 133591, 228438, 390625, 667959, 1142194, 1953125, 3339796, 5710972, 9765625, 16698983, 28554860, 48828125, 83494919, 142774303, 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 rounded down: A017979 (k=2), A017982 (k=3), A017985 (k=4), this sequence (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(5^(n/3)): n in [0..50]]; // Vincenzo Librandi, Jan 06 2014

Table[Floor[5^(n/3)], {n, 0, 40}] (* Vincenzo Librandi, Jan 06 2014 *)
Floor[Surd[5,3]^Range[0,40]] (* Harvey P. Dale, Jul 05 2022 *)

More terms From Vincenzo Librandi, Jan 06 2014

A017991 Powers of cube root of 6 rounded down.

Original entry on oeis.org

1, 1, 3, 6, 10, 19, 36, 65, 118, 216, 392, 713, 1296, 2354, 4279, 7776, 14129, 25675, 46656, 84779, 154054, 279936, 508677, 924328, 1679616, 3052064, 5545969, 10077696, 18312388, 33275819, 60466176, 109874333, 199654914, 362797056, 659246001

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 rounded down: A017979 (k=2), A017982 (k=3), A017985 (k=4), A017988 (k=5), this sequence (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(6^(n/3)): n in [0..50]]; // Vincenzo Librandi, Jan 06 2014

Table[Floor[6^(n/3)], {n, 0, 40}] (* Vincenzo Librandi, Jan 06 2014 *)
Floor[CubeRoot[6]^Range[0,40]]

More terms from Vincenzo Librandi, Jan 06 2014

A017994 Powers of cube root of 7 rounded down.

Original entry on oeis.org

1, 1, 3, 7, 13, 25, 49, 93, 179, 343, 656, 1255, 2401, 4592, 8785, 16807, 32150, 61501, 117649, 225054, 430513, 823543, 1575381, 3013595, 5764801, 11027667, 21095169, 40353607, 77193673, 147666184, 282475249, 540355712, 1033663291, 1977326743, 3782489985

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 rounded down: A017979 (k=2), A017982 (k=3), A017985 (k=4), A017988 (k=5), A017991 (k=6), this sequence (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(7^(n/3)): n in [0..50]]; // Vincenzo Librandi, Jan 06 2014

Table[Floor[7^(n/3)], {n, 0, 40}] (* Vincenzo Librandi, Jan 06 2014 *)
Floor[Surd[7,3]^Range[0,40]] (* Harvey P. Dale, Apr 05 2019 *)

More terms from Vincenzo Librandi, Jan 06 2014

A018000 Powers of cube root of 9 rounded down.

Original entry on oeis.org

1, 2, 4, 9, 18, 38, 81, 168, 350, 729, 1516, 3154, 6561, 13647, 28387, 59049, 122826, 255490, 531441, 1105441, 2299411, 4782969, 9948976, 20694704, 43046721, 89540787, 186252344, 387420489, 805867091, 1676271101, 3486784401, 7252803826, 15086439912

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 rounded down: A017979 (k=2), A017982 (k=3), A017985 (k=4), A017988 (k=5), A017991 (k=6), A017994 (k=7), this sequence (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(9^(n/3)): n in [0..50]]; // Vincenzo Librandi, Jan 06 2014

A018000:=n->floor(9^(n/3)); seq(A018000(n), n=0..50); # Wesley Ivan Hurt, Jan 16 2014

Table[Floor[9^(n/3)], {n, 0, 40}] (* Vincenzo Librandi, Jan 06 2014 *)

More terms from Vincenzo Librandi, Jan 06 2014

A018003 Powers of cube root of 10 rounded down.

Original entry on oeis.org

1, 2, 4, 10, 21, 46, 100, 215, 464, 1000, 2154, 4641, 10000, 21544, 46415, 100000, 215443, 464158, 1000000, 2154434, 4641588, 10000000, 21544346, 46415888, 100000000, 215443469, 464158883, 1000000000, 2154434690, 4641588833, 10000000000, 21544346900

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 rounded down: A017979 (k=2), A017982 (k=3), A017985 (k=4), A017988 (k=5), A017991 (k=6), A017994 (k=7), A018000 (k=9),this sequence (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(10^(n/3)): n in [0..50]]; // Vincenzo Librandi, Jan 06 2014

A018003:=n->floor(10^(n/3)); seq(A018003(n), n=0..40); # Wesley Ivan Hurt, Jun 23 2014

Table[Floor[10^(n/3)], {n, 0, 40}] (* Vincenzo Librandi, Jan 06 2014 *)

PARI
```
a(n) = floor(10^(n/3))
```

a(n) = floor( 10^(n/3) ).

More terms from Vincenzo Librandi, Jan 06 2014

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A017979 Powers of cube root of 2 rounded down.

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A018007 Powers of cube root of 11 rounded to nearest integer.

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A018024 Powers of cube root of 17 rounded down.

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A017982 Powers of cube root of 3 rounded down.

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A017985 Powers of cube root of 4 rounded down.

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A017988 Powers of cube root of 5 rounded down.

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A017991 Powers of cube root of 6 rounded down.

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A017994 Powers of cube root of 7 rounded down.

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