A011279 -id:A011279 - cp's OEIS frontend

A037124 Numbers that contain only one nonzero digit.

1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 20, 30, 40, 50, 60, 70, 80, 90, 100, 200, 300, 400, 500, 600, 700, 800, 900, 1000, 2000, 3000, 4000, 5000, 6000, 7000, 8000, 9000, 10000, 20000, 30000, 40000, 50000, 60000, 70000, 80000, 90000, 100000

Offset: 1

Vasiliy Danilov (danilovv(AT)usa.net), Jun 15 1998

Starting with 1: next greater number not containing the highest digit (see also A098395). - Reinhard Zumkeller, Oct 31 2004
A061116 is a subsequence. - Reinhard Zumkeller, Mar 26 2008
Subsequence of A193460. - Reinhard Zumkeller, Jul 26 2011

Reinhard Zumkeller, Table of n, a(n) for n = 1..1000
Michael Maltenfort, Characterizing Additive Systems, The American Mathematical Monthly, Vol. 124, No. 2 (2017), pp. 132-148.
Index entries for 10-automatic sequences.

Cf. A000005, A000079, A011279, A038754, A051885, A055640, A061116, A133464, A138707, A140730, A140740, A193459, A193460.

a037124 n = a037124_list !! (n-1)
a037124_list = f [1..9] where f (x:xs) = x : f (xs ++ [10*x])
-- Reinhard Zumkeller, May 03 2011

[((n mod 9)+1) * 10^Floor(n/9): n in [0..50]]; // Vincenzo Librandi, Nov 11 2014

Table[(10^Floor[(n - 1)/9])*(n - 9*Floor[(n - 1)/9]), {n, 1, 50}] (* José de Jesús Camacho Medina, Nov 10 2014 *)
Array[(Mod[#, 9] + 1) * 10^Floor[#/9] &, 50, 0] (* Paolo Xausa, Oct 10 2024 *)

is(n)=n>0 && n/10^valuation(n,10)<10 \\ Charles R Greathouse IV, Jan 29 2017

def A037124(n):
    a, b = divmod(n-1,9)
    return 10**a*(b+1) # Chai Wah Wu, Oct 16 2024

a(n) = (((n - 1) mod 9) + 1) * 10^floor((n - 1)/9). E.g., a(40) = ((39 mod 9) + 1) * 10^floor(39/9) = (3 + 1) * 10^4 = 40000. - Carl R. White, Jan 08 2004
a(n) = A051885(n-1) + 1. - Reinhard Zumkeller, Jan 03 2008, Jul 10 2011
A138707(a(n)) = A000005(a(n)). - Reinhard Zumkeller, Mar 26 2008
From Reinhard Zumkeller, May 26 2008: (Start)
a(n+1) = a(n) + a(n - n mod 9).
a(n) = A140740(n+9, 9). (End)
A055640(a(n)) = 1. - Reinhard Zumkeller, May 03 2011
A193459(a(n)) = A000005(a(n)). - Reinhard Zumkeller, Jul 26 2011
Sum_{n>0} 1/a(n)^s = (10^s)*(zeta(s) - zeta(s,10))/(10^s-1), with (s>1). - Enrique Pérez Herrero, Feb 05 2013
a(n) = (10^floor((n - 1)/9))*(n - 9*floor((n - 1)/9)). - José de Jesús Camacho Medina, Nov 10 2014
From Chai Wah Wu, May 28 2016: (Start)
a(n) = 10*a(n-9).
G.f.: x*(9*x^8 + 8*x^7 + 7*x^6 + 6*x^5 + 5*x^4 + 4*x^3 + 3*x^2 + 2*x + 1)/(1 - 10*x^9). (End)
a(n) ≍ 1.2589...^n, where the constant is A011279. (f ≍ g when f << g and g << f, that is, there are absolute constants c,C > 0 such that for all large n, |f(n)| <= c|g(n)| and |g(n)| <= C|f(n)|.) - Charles R Greathouse IV, Mar 11 2021
Sum_{n>=1} 1/a(n) = 7129/2268. - Amiram Eldar, Jan 21 2022

A130084 Smallest number whose tenth power has at least n digits.

Original entry on oeis.org

1, 2, 2, 2, 3, 4, 4, 6, 7, 8, 10, 13, 16, 20, 26, 32, 40, 51, 64, 80, 100, 126, 159, 200, 252, 317, 399, 502, 631, 795, 1000, 1259, 1585, 1996, 2512, 3163, 3982, 5012, 6310, 7944, 10000, 12590, 15849, 19953, 25119, 31623, 39811, 50119, 63096, 79433, 100000

Offset: 1

Klaus Brockhaus, May 07 2007

Powers of tenth root of 10 rounded up.

			3^10 = 59049 has five digits, 4^10 = 1048576 has seven digits, hence a(6) = a(7) = 4.

Vincenzo Librandi, Table of n, a(n) for n = 1..1000

Cf. A011279, A011557 (powers of 10), A017936 (smallest number whose square has n digits), A018005 (smallest number whose cube has n digits), A018074 (smallest number whose fourth power has n digits), A018143 (smallest number whose fifth power has n digits), A130080 to A130083 (smallest number whose sixth ... ninth power has n digits).

[Ceiling(Root(10^(n-1),10)): n in [1..51]];

Table[(Ceiling[10^((n - 1)/10)]), {n, 1, 60}] (* Vincenzo Librandi, Sep 20 2013 *)

from sympy import integer_nthroot
def A130084(n): return (lambda x:x[0]+(not x[1]))(integer_nthroot(10**(n-1),10)) # Chai Wah Wu, Jun 20 2024

a(n) = ceiling(10^((n-1)/10)).

A011289 Decimal expansion of 20th root of 10.

Original entry on oeis.org

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

Offset: 1

N. J. A. Sloane

In many engineering branches, ratio of two "field" amplitudes corresponding to 1 dB power ratio. For a more detailed description, see A011279. - Stanislav Sykora, Apr 02 2012

Vincenzo Librandi, Table of n, a(n) for n = 1..1000

Cf. A011279.

RealDigits[N[10^(1/20),200]][[1]] (* Vladimir Joseph Stephan Orlovsky, Jan 25 2012 *)
RealDigits[Surd[10,20],10,120][[1]] (* Harvey P. Dale, Jul 30 2023 *)

sqrtn(10,20) \\ Charles R Greathouse IV, Apr 14 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

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A037124 Numbers that contain only one nonzero digit.

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A130084 Smallest number whose tenth power has at least n digits.

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A011289 Decimal expansion of 20th root of 10.

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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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