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.
5, 11, 17, 41, 307, 1447, 2377, 3163, 3253, 3457, 4783, 5653, 6547, 7873, 9007, 11171, 11827, 16061, 16187, 19423, 20743, 20897, 21313, 21517, 26107, 27103, 29017, 29021, 33613, 34123, 34841, 34843, 36011, 38917, 39227, 40693, 41177, 47737, 51341, 55213
Offset: 1
Examples
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.
Links
- Michael S. Branicky, Table of n, a(n) for n = 1..10000
Crossrefs
Cf. A174858.
Programs
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Mathematica
Select[Partition[Prime[Range[6000]],3,1],#[[3]]-#[[1]]==6&&PrimeQ[FromDigits[Flatten[ IntegerDigits/@ #]]]&][[;;,1]] (* Harvey P. Dale, Aug 21 2024 *)
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Python
from itertools import islice from sympy import isprime, nextprime def agen(): # generator of terms p, q, r = 2, 3, 5 while True: if (q == p+2 or q == p+4) and r == p+6: if isprime(int(str(p) + str(q) + str(r))): yield p p, q, r = q, r, nextprime(r) print(list(islice(agen(), 41))) # Michael S. Branicky, Aug 18 2024