A038378 -id:A038378 - cp's OEIS frontend

A043537 Number of distinct base-10 digits of n.

1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2

Offset: 1

Clark Kimberling

a(A000079(A130694(n))) = 10. - Reinhard Zumkeller, Jul 29 2007
a(A000290(A016070(n))) = 2. - Reinhard Zumkeller, Aug 05 2010
a(n) = 10 for almost all n. - Charles R Greathouse IV, Oct 02 2013

R. Zumkeller, Table of n, a(n) for n = 1..10000

Cf. A047726, A118668, A119797, A119798, A119799, A119823, A038378, A076493, A055642, A178788.

import Data.List (nub)
a043537 = length . nub . show  -- Reinhard Zumkeller, Apr 16 2011

A043537 := proc(n)
        convert(convert(n,base,10),set) ;
        nops(%) ;
end proc: # R. J. Mathar, Dec 22 2012

Count[DigitCount@ #, n_ /; n > 0] & /@ Range@ 120 (* Michael De Vlieger, Aug 29 2015 *)

a(n)=#vecsort(digits(n),,8) \\ Charles R Greathouse IV, Oct 02 2013

def A043537(n): return len(set(str(n))) # Dimiter Skordev, Oct 02 2021

A007809 Smallest prime with n distinct digits.

Original entry on oeis.org

2, 13, 103, 1039, 10243, 102359, 1023467, 10234589, 102345689

Offset: 1

N.B. Backhouse (sx52(AT)liverpool.ac.uk)

J.-M. De Koninck, Ces nombres qui nous fascinent, Entry 1039, p.126, Ellipses, Paris 2008. [From Lekraj Beedassy, Oct 12 2008]

Cf. A038378, A007810, A071360, A071361, A071362, A071363.

Table[Module[{k=NextPrime[10^n]},While[Max[DigitCount[k]]>1,k=NextPrime[k]];k],{n,0,8}] (* Harvey P. Dale, May 27 2025 *)

A007809(n,p=A038378(n))={until(isprime(p),while(#Set(digits(p++))M. F. Hasler, May 04 2017

from sympy import nextprime
def a(n):
  p = nextprime(10**(n-1))
  while len(set(str(p))) < n: p = nextprime(p)
  return p
for n in range(1, 10):
  print(a(n), end=", ") # Michael S. Branicky, Feb 13 2021

Corrected by Jud McCranie, Jan 03 2001

A101599 a(n) = binomial coefficient C(m,k) with minimal (m,k) and exactly n distinct digits in decimal representation.

Original entry on oeis.org

1, 10, 126, 1287, 12870, 125970, 1352078, 84672315, 137846528820, 6499270398159

Offset: 1

Reinhard Zumkeller, Dec 08 2004

			A101598(49,17) = A043537(6499270398159) = 10.

Cf. A038378.

A081716 Smallest number x such that phi(x)=A000010(x) has exactly n different decimal digits.

Original entry on oeis.org

2, 11, 103, 1033, 10247, 102359, 1023487, 10234759, 102345979, 1023475969

Offset: 1

Labos Elemer, Apr 04 2003

			phi applied to the sequence gives: 1, 10, 102, 1032, 10246, 102358, 1023486, 10234758, 102345978, ...

Cf. A007809, A038378, A000010.

f[x_] := Length[Union[IntegerDigits[x]]]
t=Table[0, {10}];
Do[s=f[n]; If[PrimeQ[n]&&s<11&&t[[s]]==0,
t[[s]]=n], {n, 1, 10000000000}];

a(10) from Donovan Johnson, Feb 05 2010

A356726 Integers which have in Roman numerals more distinct symbols than any smaller number.

Original entry on oeis.org

1, 4, 14, 44, 144, 444, 1444

Offset: 1

Alain Cousquer, Aug 24 2022

Indices of record highs in A057226.
Smallest number whose Roman notation has exactly n distinct symbols.
The sequence is finite because 1444 is the smallest number using the symbols I,V,X,L,C,D,M.

			For n = 3, a(3) = 14 because 14 = XIV which is the smallest number with 3 symbols in Roman notation.

Cf. A057226, A038378.

kmax=1500; a={}; n=1; For[k=1, k<=kmax, k++, If[Length[DeleteDuplicates[Characters[RomanNumeral[k]]]] == n, AppendTo[a, k]; n++; k=1]]; a (* Stefano Spezia, Aug 26 2022 *)

cp's OEIS Frontend

A043537 Number of distinct base-10 digits of n.

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A007809 Smallest prime with n distinct digits.

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A101599 a(n) = binomial coefficient C(m,k) with minimal (m,k) and exactly n distinct digits in decimal representation.

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A081716 Smallest number x such that phi(x)=A000010(x) has exactly n different decimal digits.

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Mathematica

Extensions

A356726 Integers which have in Roman numerals more distinct symbols than any smaller number.

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Mathematica