A337840 a(n) is the decimal place of the start of the first occurrence of n in the decimal expansion of n^(1/n).
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
Examples
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.
Links
- Chai Wah Wu, Table of n, a(n) for n = 1..10000
Crossrefs
Programs
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Mathematica
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 *)
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PARI
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 -
Python
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
Extensions
More terms from Amiram Eldar, Sep 25 2020
Comments