A138707 -id:A138707 - 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

A061116 Numbers coprime to each of their decimal digits.

Original entry on oeis.org

11, 13, 17, 19, 21, 23, 27, 29, 31, 37, 41, 43, 47, 49, 51, 53, 57, 59, 61, 67, 71, 73, 79, 81, 83, 87, 89, 91, 97, 111, 113, 117, 119, 121, 127, 131, 133, 137, 139, 141, 143, 149, 151, 157, 161, 163, 167, 169, 171, 173, 177, 179, 181, 187, 191, 193, 197, 199, 211

Offset: 1

Amarnath Murthy, Apr 21 2001

A138707(a(n)) = 1; subsequence of A138708. - Reinhard Zumkeller, Mar 26 2008

			27 is a member as 2 and 7 both are coprime to 27. 53 is a member as 5 and 3 both are coprime to 53.

Michael S. Branicky, Table of n, a(n) for n = 1..10000
Index entries for 10-automatic sequences.

Cf. A138707, A138708.

for n from 2 to 500 do it1 := convert(n, base, 10): flag := 1: for k from 1 to nops(it1) do if igcd(n, it1[k])<>1 then flag := 0 fi: od: if flag=1 then printf(`%d,`,n) fi: od:

Select[Range[11, 191, 2], CoprimeQ[Product[i, {i, IntegerDigits[#]}], #] &] (* Arkadiusz Wesolowski, May 19 2012 *)

from math import gcd
def ok(n): return n > 1 and all(gcd(n, int(d)) == 1 for d in str(n))
print([k for k in range(212) if ok(k)]) # Michael S. Branicky, Nov 13 2021

More terms from James Sellers, Apr 23 2001

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A138708 Numbers m such that A138707(m) = 1.

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A037124 Numbers that contain only one nonzero digit.

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A061116 Numbers coprime to each of their decimal digits.

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