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 A073532 Number of n-digit primes with all digits distinct. 7
 4, 20, 97, 510, 2529, 10239, 33950, 90510, 145227, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 (list; graph; refs; listen; history; text; internal format)
 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 decimal digits, so a[x]=0 for x>=10. - Labos Elemer, Oct 25 2004; Robert G. Wilson v, Jul 25 2008 Entries checked by Robert G. Wilson v, Jul 25 2008 LINKS 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 Cf. A073531, A006880, A006879, A098224-A098227, A140532. Sequence in context: A240778 A293710 A098225 * A178874 A103771 A005054 Adjacent sequences:  A073529 A073530 A073531 * A073533 A073534 A073535 KEYWORD base,nonn AUTHOR Zak Seidov, Aug 29 2002 EXTENSIONS Edited by N. J. A. Sloane, Aug 14 2007 STATUS approved

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Last modified June 12 16:18 EDT 2021. Contains 344959 sequences. (Running on oeis4.)