A011092 -id:A011092 - cp's OEIS frontend

A018133 Powers of fifth root of 7 rounded to nearest integer.

1, 1, 2, 3, 5, 7, 10, 15, 22, 33, 49, 72, 107, 157, 232, 343, 506, 747, 1102, 1627, 2401, 3543, 5229, 7717, 11389, 16807, 24803, 36604, 54019, 79720, 117649, 173623, 256229, 378135, 558042, 823543

Offset: 0

N. J. A. Sloane

nonn

Cf. A011092.

Round[Surd[7,5]^Range[0,40]] (* Harvey P. Dale, Jul 27 2021 *)

from gmpy2 import iroot_rem
def A018133(n):
    i, j = iroot_rem(7**n,5)
    return int(i)+int(j<<5>=10*i*((i*((i*(i+1)<<1)+1)<<2)+1)+1) # Chai Wah Wu, Jun 20 2024

A011183 Decimal expansion of 5th root of 98.

Original entry on oeis.org

2, 5, 0, 1, 7, 5, 7, 5, 2, 7, 1, 4, 0, 8, 4, 3, 5, 1, 3, 0, 8, 7, 2, 4, 4, 8, 5, 4, 9, 2, 6, 2, 9, 8, 3, 7, 2, 0, 6, 0, 4, 5, 7, 4, 7, 0, 6, 8, 0, 9, 7, 7, 9, 7, 9, 9, 3, 2, 6, 1, 3, 5, 7, 8, 6, 5, 1, 7, 1, 6, 3, 9, 7, 0, 0, 6, 1, 1, 8, 9, 9, 7, 4, 2, 2, 8, 0, 0, 7, 9, 8, 8, 3, 3, 3, 9, 8, 2, 7

Offset: 1

N. J. A. Sloane

Ivan Panchenko, Table of n, a(n) for n = 1..1000

RealDigits[Surd[98,5],10,120][[1]] (* Harvey P. Dale, Mar 06 2014 *)

Equals A005531*A011092^2 . - R. J. Mathar, Aug 27 2024

A018132 Powers of fifth root of 7 rounded down.

Original entry on oeis.org

1, 1, 2, 3, 4, 7, 10, 15, 22, 33, 49, 72, 106, 157, 232, 343, 506, 747, 1102, 1626, 2401, 3543, 5229, 7717, 11388, 16807, 24803, 36604, 54019, 79720, 117649, 173623, 256228, 378135, 558041, 823543, 1215362, 1793599, 2646946, 3906292, 5764801, 8507538, 12555197, 18528622, 27344044, 40353607, 59552770

Offset: 0

N. J. A. Sloane

nonn

Vincenzo Librandi, Table of n, a(n) for n = 0..2000

Cf. A011092.

[Floor(7^(n/5)) : n in [0..60]]; // Vincenzo Librandi, Jun 13 2025

Floor[Surd[7,5]^Range[0,40]] (* Harvey P. Dale, Apr 06 2018 *)
Table[Floor[(7^(1/5))^n], {n, 0, 50}] (* Vincenzo Librandi, Jun 13 2025 *)

A281143 Decimal expansion of 10!^(1/10).

Original entry on oeis.org

4, 5, 2, 8, 7, 2, 8, 6, 8, 8, 1, 1, 6, 7, 6, 4, 7, 6, 2, 2, 0, 3, 3, 0, 9, 3, 3, 7, 1, 9, 5, 5, 0, 8, 7, 9, 3, 4, 9, 8, 6, 3, 1, 6, 7, 6, 0, 8, 9, 3, 9, 0, 4, 6, 2, 8, 8, 6, 1, 1, 4, 7, 6, 0, 4, 6, 9, 2, 6, 2, 5, 5, 3, 8, 4, 5, 4, 1, 2, 8, 3, 9, 0, 7, 5, 1, 7, 7, 2, 4, 6, 5, 8, 2, 8, 8, 4, 9, 9, 4, 5, 8, 3, 1, 7

Offset: 1

Robert G. Wilson v, Jan 15 2017

Base b such that log_b 10! = 10.

Inspired by the idea of utilizing the log scaled to 10! being 10, i.e., log_b 10! = 10, therefore b = 2^(4/5)*3^(2/5)*5^(1/5)*7^(1/10).

			4.52872868811676476220330933719550879349863167608939046288611476046926255...

Cf. A002193, A005486, A005534, A011020, A011092, A011094, A011101.

RealDigits[2^(4/5) 3^(2/5) 5^(1/5) 7^(1/10), 10, 111][[1]] (* or *)
RealDigits[Solve[Log[b, 10!] == 10, b][[1, 1, 2]], 10, 105][[1]]

Equals A011101 * A011094 * A005534 * A011092.

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A018133 Powers of fifth root of 7 rounded to nearest integer.

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A011183 Decimal expansion of 5th root of 98.

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A018132 Powers of fifth root of 7 rounded down.

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A281143 Decimal expansion of 10!^(1/10).

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