A007809 Smallest prime with n distinct digits.

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

Offset: 1

Author

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

Keywords

• nonn
• fini
• base
• full

References

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

Crossrefs

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

Programs

Mathematica

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

PARI

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

Python

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

Extensions

Corrected by Jud McCranie, Jan 03 2001