A002581 -id:A002581 - cp's OEIS frontend

A271836 Decimal expansion of 3^(1/3) / 2^(1/6).

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

Offset: 1

Wesley Ivan Hurt, Apr 15 2016

Used in a formula for a regular octahedron, a = 3^(1/3)/2^(1/6) * V^(1/3), where a is the edge length and V^(1/3) is the cube root of the volume.

An algebraic number of degree 6 and denominator 2; minimal polynomial is 2x^6 - 9. - Charles R Greathouse IV, Apr 18 2016

			1.2848982934253252956716...

Chai Wah Wu, Table of n, a(n) for n = 1..10000
Wikipedia, Octahedron
Index entries for algebraic numbers, degree 6

Cf. A002581, A010768.

Maple
```
Digits:=100: evalf(3^(1/3)/2^(1/6));
```
Mathematica
```
RealDigits[N[3^(1/3)/2^(1/6), 100]]
```

3^(1/3) / 2^(1/6) \\ Altug Alkan, Apr 15 2016

sqrtn(9/2,6) \\ Charles R Greathouse IV, Apr 18 2016

Equals A002581 / A010768.

A307513 Beatty sequence for 1/log(2).

Original entry on oeis.org

1, 2, 4, 5, 7, 8, 10, 11, 12, 14, 15, 17, 18, 20, 21, 23, 24, 25, 27, 28, 30, 31, 33, 34, 36, 37, 38, 40, 41, 43, 44, 46, 47, 49, 50, 51, 53, 54, 56, 57, 59, 60, 62, 63, 64, 66, 67, 69, 70, 72, 73, 75, 76, 77, 79, 80, 82, 83, 85, 86, 88, 89, 90, 92, 93, 95, 96, 98, 99, 100, 102, 103, 105, 106, 108, 109, 111, 112, 113, 115

Offset: 1

R. J. Mathar, Apr 12 2019

Very similar to A059539 because A002581 is close to A007525.

Cf. A007525.

a(n) = floor(n*A007525).

A166986(n) = 2*a(n+2)-4.

A337840 a(n) is the decimal place of the start of the first occurrence of n in the decimal expansion of n^(1/n).

Original entry on oeis.org

0, 4, 10, 1, 38, 6, 9, 4, 12, 17, 26, 0, 264, 144, 107, 101, 101, 4, 78, 68, 36, 86, 11, 17, 147, 151, 205, 50, 55, 26, 307, 88, 94, 180, 177, 61, 113, 244, 280, 37, 110, 38, 285, 101, 124, 223, 243, 25, 86, 116, 66, 77, 146, 283, 3, 60, 20, 82, 27, 146, 82, 140

Offset: 1

William Phoenix Marcum, Sep 25 2020

Does a(n) exist for all n? Some relatively large values: a(1021) = 67714, a(1111) = 64946. - Chai Wah Wu, Oct 07 2020

			For n = 1, 1^(1/1) = 1.0000000, so a(1) is 0.
For n = 12, 12^(1/12) ~= 1.2300755, so a(12) = 0.

Chai Wah Wu, Table of n, a(n) for n = 1..10000

Cf. A177715.

Decimal expansions of some n^(1/n): A002193, A002581, A005534, A011215, A011231, A011247, A011263, A011279, A011295, A011311, A011327, A011343, A011359.

max = 3000; a[n_] := SequencePosition[RealDigits[n^(1/n), 10, max][[1]], IntegerDigits[n]][[1, 1]] - 1; Array[a, 100] (* Amiram Eldar, Sep 25 2020 *)

a(n) = {if (n==1, 0, my(p=10000); default(realprecision, p+1); my(x = floor(10^p*n^(1/n)), d = digits(x), nb = #Str(n)); for(k=1, #d-nb+1, my(v=vector(nb, i, d[k+i-1])); if (fromdigits(v) == n, return(k-1));); error("not found"););} \\ Michel Marcus, Sep 30 2020

import gmpy2
from gmpy2 import mpfr, digits, root
gmpy2.get_context().precision=10**5
def A337840(n): # increase precision if -1 is returned
    return digits(root(mpfr(n),n))[0].find(str(n)) # Chai Wah Wu, Oct 07 2020

More terms from Amiram Eldar, Sep 25 2020

A384307 Decimal expansion of sqrt(6/Pi)*Gamma(2/3)/3^(1/3).

Original entry on oeis.org

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

Offset: 1

Stefano Spezia, May 25 2025

			1.2975280711403750650601222740909286296388090291...

Andrej Srakar, Short survey of results and open problems for parking problems on random trees, arXiv:2505.15826 [math.PR], 2025. See p. 10.

Cf. A002581, A073006, A132696.

RealDigits[Sqrt[6/Pi]Gamma[2/3]/3^(1/3),10,100][[1]]

Equals sqrt(A132696)*A073006/A002581.

cp's OEIS Frontend

A271836 Decimal expansion of 3^(1/3) / 2^(1/6).

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A307513 Beatty sequence for 1/log(2).

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A337840 a(n) is the decimal place of the start of the first occurrence of n in the decimal expansion of n^(1/n).

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A384307 Decimal expansion of sqrt(6/Pi)*Gamma(2/3)/3^(1/3).

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