A010589 -id:A010589 - cp's OEIS frontend

A018025 Powers of cube root of 17 rounded to nearest integer.

1, 3, 7, 17, 44, 112, 289, 743, 1911, 4913, 12633, 32482, 83521, 214756, 552198, 1419857, 3650852, 9387369, 24137569, 62064487, 159585272, 410338673, 1055096276, 2712949630, 6975757441, 17936636689, 46120143717, 118587876497, 304922823712, 784042443182

Offset: 0

N. J. A. Sloane

nonn

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

Cf. A010589, A018024, A018026, 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), A018007 (k=11), A018010 (k=12), A018013 (k=13), A018016 (k=14), A018019 (k=15), A018022 (k=16), this sequence (k=17), A018028 (k=18), A018031 (k=19), A018034 (k=20), A018037 (k=21), A018040 (k=22), A018043 (k=23), A018046 (k=24).

[Round(17^(n/3)): n in [0..40]]; // Vincenzo Librandi, Jan 08 2014

Table[Round[17^(n/3)], {n, 0, 40}] (* Vincenzo Librandi, Jan 08 2014 *)

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

from sympy import integer_nthroot
def A018025(n): return -integer_nthroot(m:=17**n,3)[0]+integer_nthroot(m<<3,3)[0] # Chai Wah Wu, Jun 18 2024

More terms from Michel Marcus, Nov 23 2013

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

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

A010247 Continued fraction for cube root of 17.

Original entry on oeis.org

2, 1, 1, 3, 138, 1, 1, 3, 2, 3, 1, 1, 207, 1, 2, 2, 1, 1, 1, 1, 2, 4, 9, 1, 2, 4, 1, 1, 3, 4, 277, 2, 5, 3, 3, 3, 1, 1, 1, 1, 13, 2, 15, 20, 2, 1, 1, 1, 1, 1, 2, 1, 2, 18, 2, 4, 1, 22, 20, 51, 23, 2, 1, 3, 2, 204, 1, 2, 3, 1, 4, 1, 3, 76

Offset: 0

N. J. A. Sloane

G. Xiao, Contfrac

Cf. A010589.

contfrac(17^(1/3)) \\ Michel Marcus, Nov 23 2013

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A018025 Powers of cube root of 17 rounded to nearest integer.

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A018024 Powers of cube root of 17 rounded down.

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A018026 Powers of cube root of 17 rounded up.

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A010247 Continued fraction for cube root of 17.

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