A098224 Number of primes <=10^n in which decimal digits are all distinct.

4, 24, 121, 631, 3160, 13399, 47349, 137859, 283086, 283086, 283086, 283086, 283086, 283086, 283086, 283086, 283086, 283086, 283086, 283086, 283086, 283086, 283086, 283086, 283086, 283086, 283086, 283086, 283086, 283086, 283086, 283086, 283086, 283086, 283086

Offset: 1

Author

Labos Elemer, Oct 26 2004

Keywords

• base
• nonn

Comments

Partial sums of A073532. - Lekraj Beedassy, Aug 02 2008

No number with more than 10 digits can have all of its decimal digits distinct, and no number that uses all ten distinct decimal digits can be prime (because the sum of all ten decimal digits is 45 so any such number is divisible by 3). Therefore, every term in the sequence from and after a(9) is the same, i.e., 283086. - Harvey P. Dale, Dec 12 2010

Crossrefs

Cf. A006880, A006879, A073532, A098226-A098227.

Programs

Mathematica

okQ[n_]:=Max[DigitCount[n]]==1
Table[Length[Select[Prime[Range[PrimePi[10^i]]],okQ]],{i,9}] (* Harvey P. Dale, Dec 12 2010 *)

Python

from sympy import sieve
def distinct_digs(n): s = str(n); return len(s) == len(set(s))
def aupton(terms):
  ps, alst = 0, []
  for n in range(1, terms+1):
    if n >= 10: alst.append(ps); continue
    ps += sum(distinct_digs(p) for p in sieve.primerange(10**(n-1), 10**n))
    alst.append(ps)
  return alst
print(aupton(35)) # Michael S. Branicky, Apr 24 2021

Formula

a(n) = 283086 for n >= 9.