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A371509 a(n) is the smallest prime that becomes composite if any single digit of its base-(2n+1) expansion is changed to a different digit (but not to zero).

%I A371509 #15 Mar 26 2024 16:59:53
%S A371509 2,67,223,2789,701,2423,243367,10513,10909,2114429,68543,181141,
%T A371509 6139219,114493,356479,399946711,22549349,8371249,660040873,12088631,
%U A371509 3352003
%N A371509 a(n) is the smallest prime that becomes composite if any single digit of its base-(2n+1) expansion is changed to a different digit (but not to zero).
%C A371509 Bisection of A323745. a(n) <= A371475(n) with equality for some values of n.
%F A371509 a(n) = A323745(2n+1).
%F A371509 a(n) <= A371475(n).
%o A371509 (Python)
%o A371509 from sympy import isprime, nextprime
%o A371509 from sympy.ntheory import digits
%o A371509 def A371509(n):
%o A371509     if n == 1: return 2
%o A371509     p, r = 5, (n<<1)+1
%o A371509     while True:
%o A371509         m = 1
%o A371509         for j in digits(p,r)[:0:-1]:
%o A371509             for k in range(2-(j&1),r,2):
%o A371509                 if k!=j and isprime(p+(k-j)*m):
%o A371509                     break
%o A371509             else:
%o A371509                 m *= r
%o A371509                 continue
%o A371509             break
%o A371509         else:
%o A371509             return p
%o A371509         p = nextprime(p)
%Y A371509 Cf. A186995, A323745, A371475.
%K A371509 nonn,more,base
%O A371509 1,1
%A A371509 _Chai Wah Wu_, Mar 25 2024