OFFSET
1,1
COMMENTS
For any base b the number of distinct-digit primes is finite. For base 10, the maximal distinct-digit prime is 987654103; for any larger prime at least two digits coincide. The number of distinct-digit integers is also finite, see A073531.
No such primes exist with 10 or more distinct decimal digits, so a(n) = 0 for n >= 10. - Labos Elemer, Oct 25 2004; Robert G. Wilson v, Jul 25 2008
EXAMPLE
a(3)=97 because there are 97 three-digit primes with distinct digits: 103, 107, 109, 127, 137, 139, 149, 157, 163, 167, 173, 179, 193, 197,239, 241, 251, 257, 263, 269, 271, 281, 283, 293,307, 317, 347, 349, 359, 367, 379, 389, 397, 401, 409, 419, 421, 431, 439, 457, 461, 463, 467, 479, 487, 491, 503, 509, 521, 523, 541, 547, 563, 569, 571, 587, 593, 601, 607, 613, 617, 619, 631, 641, 643, 647, 653, 659, 673, 683, 691, 701, 709, 719, 739, 743, 751, 761, 769, 809, 821, 823, 827, 829, 839, 853, 857, 859, 863, 907, 937, 941, 947, 953, 967, 971, 983.
MATHEMATICA
lst = {}; Do[p = Prime@ n; If[ Union[Length /@ Split@ Sort@ IntegerDigits@ p] == {1}, AppendTo[lst, p]], {n, PrimePi[10^9]}]; Table[ Length@ Select[lst, 10^n < # < 10^(n + 1) &], {n, 0, 9}] (* Robert G. Wilson v, Jul 25 2008 *)
PROG
(Python)
from itertools import permutations
from sympy import isprime, primerange
def distinct_digs(n): s = str(n); return len(s) == len(set(s))
def a(n):
if n >= 10: return 0
return sum(isprime(int("".join(p))) for p in permutations("0123456789", n) if p[0] != '0')
print([a(n) for n in range(1, 31)]) # Michael S. Branicky, Apr 20 2021
CROSSREFS
KEYWORD
base,nonn
AUTHOR
Zak Seidov, Aug 29 2002
EXTENSIONS
Edited by N. J. A. Sloane, Aug 14 2007
Entries checked by Robert G. Wilson v, Jul 25 2008
STATUS
approved