A375313 - OEIS

%I #18 Aug 21 2024 14:53:08

%S 5,11,17,41,307,1447,2377,3163,3253,3457,4783,5653,6547,7873,9007,

%T 11171,11827,16061,16187,19423,20743,20897,21313,21517,26107,27103,

%U 29017,29021,33613,34123,34841,34843,36011,38917,39227,40693,41177,47737,51341,55213

%N 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 Michael S. Branicky, <a href="/A375313/b375313.txt">Table of n, a(n) for n = 1..10000</a>

%e 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 Select[Partition[Prime[Range[6000]],3,1],#[[3]]-#[[1]]==6&&PrimeQ[FromDigits[Flatten[ IntegerDigits/@ #]]]&][[;;,1]] (* _Harvey P. Dale_, Aug 21 2024 *)

%o (Python)

%o from itertools import islice

%o from sympy import isprime, nextprime

%o def agen(): # generator of terms

%o     p, q, r = 2, 3, 5

%o     while True:

%o         if (q == p+2 or q == p+4) and r == p+6:

%o             if isprime(int(str(p) + str(q) + str(r))):

%o                 yield p

%o         p, q, r = q, r, nextprime(r)

%o print(list(islice(agen(), 41))) # _Michael S. Branicky_, Aug 18 2024

%Y Cf. A174858.

%K nonn,base

%O 1,1

%A _James S. DeArmon_, Aug 11 2024