A011215 -id:A011215 - cp's OEIS frontend

A011200 Decimal expansion of 6th root of 5.

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

Offset: 1

N. J. A. Sloane

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

Cf. A011201 ... A011214 (other roots of 5), A011215 ... A011439 (n-th roots of 6, ..., 20) ; A011440 ... A011519 (n-th root of n = 21, ..., 100).

RealDigits[Surd[5,6],10,120][[1]] (* Harvey P. Dale, Jul 16 2013 *)

sqrtn(5,6) \\ Charles R Greathouse IV, Aug 26 2017

A011519 Decimal expansion of 100th root of 100.

Original entry on oeis.org

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

Offset: 1

N. J. A. Sloane

Vincenzo Librandi, Table of n, a(n) for n = 1..5000
M. F. Hasler, "Ranges": Index to n-th roots of x. OEIS Wiki, Aug 26 2017

Cf. A011200 ... A011214 (other roots of 5), A011215 ... A011439 (n-th roots of 6, ..., 20) ; A011440 ... A011519 (n-th root of n = 21, ..., 100).

RealDigits[N[100^(1/100), 100]][[1]] (* Vincenzo Librandi, Mar 23 2013 *)

sqrtn(100,100) \\ Charles R Greathouse IV, Apr 15 2014

A274085 Continued fraction for sixth root of 6.

Original entry on oeis.org

1, 2, 1, 6, 1, 9, 1, 1, 1, 2, 4, 9, 4, 4, 2, 2, 1, 8, 1, 2, 21, 10, 1, 13, 4, 1, 6, 2, 10, 2, 2, 3, 1, 12, 3, 2, 1, 1, 2, 1, 9, 7, 3, 1, 4, 2, 8, 1, 11, 1, 2, 4, 3, 1, 7, 6, 1, 1, 1, 11, 1, 2, 1, 9, 1, 2, 1, 2, 9, 44, 1, 1, 1, 1, 34, 1, 12, 1, 3, 2, 3, 54, 1

Offset: 0

Douglas de Araujo Smigly, Jun 09 2016

			6^(1/6) = 1 + 1/(2 + 1/(1 + 1/(6 + 1/(1 + ...)))).

Robert Israel, Table of n, a(n) for n = 0..1999
Index entries for continued fractions for constants

Cf. A011215 (decimal expansion).

numtheory:-cfracpol(x^6-6,100)[2]; # Robert Israel, Jul 31 2016

ContinuedFraction[6^(1/6), {80}] (* Alonso del Arte, Jun 18 2016 *)

default(realprecision, 210);  contfrac(6^(1/6))

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

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A011200 Decimal expansion of 6th root of 5.

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A011519 Decimal expansion of 100th root of 100.

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A274085 Continued fraction for sixth root of 6.

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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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