A011231 -id:A011231 - cp's OEIS frontend

A011186 Decimal expansion of 7th root of 4.

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

Offset: 1

N. J. A. Sloane

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

Cf. A010769, A011201, A011216, A011231, A011246, A011261, A011276, A011291, A011306, A011321, A011336, A011351, A011366, A011381, A011396, A011411, A011426.

RealDigits[4^(1/7),10,99][[1]] (* Stefano Spezia, Apr 03 2025 *)

sqrtn(4, 7) \\ Michel Marcus, Sep 04 2014

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

A375851 Decimal expansion of the 7th root of 306.

Original entry on oeis.org

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

Offset: 1

Stefano Spezia, Sep 15 2024

Calculated to 2800 digits by R. William Gosper in a 1976 contest where this task was the problem number 9.

			2.26518178629569774774567213263272411892131...

David Wells, The Penguin Dictionary of Curious and Interesting Numbers. Penguin Books, NY, 1986, Revised edition 1987. See pp. 151-152.

Fred Gruenberger, Contest 12: Countdown, Popular Computing, Vol. 4, No. 10 (1976), p. 10.
Fred Gruenberger, Contest 12 results, Popular Computing, Vol. 5, No. 3 (1977), p. 6.
Fred Gruenberger, Gosper, Popular Computing, Vol. 5, No. 5 (1977), p. 18.
Fred Gruenberger, Computer Recreations, Scientific American, Vol. 250, No. 4 (1984), pp. 19-27.

Cf. A010769, A011186, A011201, A011216, A011231, A011246, A011261, A011276, A011291, A011306, A011321, A011336, A011351, A011366, A011381, A011396, A011411, A011426.

Mathematica
```
RealDigits[306^(1/7),10,100][[1]]
```

sqrtn(306, 7) \\ Amiram Eldar, Sep 18 2024

Equals A010769*A011261*A011381. - R. J. Mathar, Sep 23 2024

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A011186 Decimal expansion of 7th root of 4.

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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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A375851 Decimal expansion of the 7th root of 306.

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