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A375313 Primes p such that the prime triple (p, p+2 or p+4, p+6) generates a prime number when the digits are concatenated.

%I A375313 #18 Aug 21 2024 14:53:08
%S A375313 5,11,17,41,307,1447,2377,3163,3253,3457,4783,5653,6547,7873,9007,
%T A375313 11171,11827,16061,16187,19423,20743,20897,21313,21517,26107,27103,
%U A375313 29017,29021,33613,34123,34841,34843,36011,38917,39227,40693,41177,47737,51341,55213
%N A375313 Primes p such that the prime triple (p, p+2 or p+4, p+6) generates a prime number when the digits are concatenated.
%H A375313 Michael S. Branicky, <a href="/A375313/b375313.txt">Table of n, a(n) for n = 1..10000</a>
%e A375313 The first term is 5, since the prime triple (p,p+2,p+6) or (5,7,11) generates the prime number 5711 when the digits are concatenated. The fifth term is 307, since the prime triple (p,p+4,p+6) or (307,311,313) generates the prime number 307311313 when the digits are concatenated.
%t A375313 Select[Partition[Prime[Range[6000]],3,1],#[[3]]-#[[1]]==6&&PrimeQ[FromDigits[Flatten[ IntegerDigits/@ #]]]&][[;;,1]] (* _Harvey P. Dale_, Aug 21 2024 *)
%o A375313 (Python)
%o A375313 from itertools import islice
%o A375313 from sympy import isprime, nextprime
%o A375313 def agen(): # generator of terms
%o A375313     p, q, r = 2, 3, 5
%o A375313     while True:
%o A375313         if (q == p+2 or q == p+4) and r == p+6:
%o A375313             if isprime(int(str(p) + str(q) + str(r))):
%o A375313                 yield p
%o A375313         p, q, r = q, r, nextprime(r)
%o A375313 print(list(islice(agen(), 41))) # _Michael S. Branicky_, Aug 18 2024
%Y A375313 Cf. A174858.
%K A375313 nonn,base
%O A375313 1,1
%A A375313 _James S. DeArmon_, Aug 11 2024