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A068803 Smaller of two consecutive primes which have no common digits.

%I A068803 #29 Jul 02 2023 17:59:36
%S A068803 2,3,5,7,19,29,37,47,59,79,97,397,499,599,1999,2999,3989,4999,29989,
%T A068803 49999,59999,79999,199999,599999,799999,2999999,4999999,5999993,
%U A068803 19999999,29999999,59999999,69999989,99999989,199999991,699999953,799999999,5999999989,6999999989
%N A068803 Smaller of two consecutive primes which have no common digits.
%C A068803 Is the sequence finite or infinite?
%C A068803 Except for 2, 3, 5, and 7, all such primes are of the form a*10^n-b with 1 <= a <= 8 and b mod 10 = 1, 3, 7 or 9. An example of a large pair is 10^101-203 and 10^101+3. The largest known pair of probable primes is 8*10^5002-6243 and 8*10^5002+14481. - _Lewis Baxter_, Mar 06 2023
%H A068803 Michael S. Branicky, <a href="/A068803/b068803.txt">Table of n, a(n) for n = 1..804</a>
%e A068803 397 is a term as 397 and 401 are two consecutive primes with no common digits.
%t A068803 First /@ Select[Partition[Prime[Range[10^6]], 2, 1], Intersection @@ IntegerDigits /@ # == {} &] (* _Jayanta Basu_, Aug 06 2013 *)
%o A068803 (PARI) isok(p) = isprime(p) && (#setintersect(Set(digits(p)), Set(digits(nextprime(p+1)))) == 0); \\ _Michel Marcus_, Mar 27 2023
%o A068803 (Python)
%o A068803 from itertools import count, islice
%o A068803 from sympy import nextprime, prevprime
%o A068803 def agen(): # generator of terms
%o A068803     yield from [2, 3, 5]
%o A068803     for d in count(2):
%o A068803         for b in range(10**(d-1), 10**d, 10**(d-1)):
%o A068803             p, q = prevprime(b), nextprime(b)
%o A068803             if set(str(p)) & set(str(q)) == set():
%o A068803                 yield p
%o A068803 print(list(islice(agen(), 40))) # _Michael S. Branicky_, May 09 2023
%Y A068803 Cf. A076490.
%K A068803 base,nonn
%O A068803 1,1
%A A068803 _Amarnath Murthy_, Mar 06 2002
%E A068803 More terms from Larry Soule (lsoule(AT)gmail.com), Jun 21 2006
%E A068803 a(36) and beyond from _Michael S. Branicky_, May 09 2023