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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.
1
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
1,1
LINKS
EXAMPLE
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.
MATHEMATICA
Select[Partition[Prime[Range[6000]], 3, 1], #[[3]]-#[[1]]==6&&PrimeQ[FromDigits[Flatten[ IntegerDigits/@ #]]]&][[;; , 1]] (* Harvey P. Dale, Aug 21 2024 *)
PROG
(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
CROSSREFS
Cf. A174858.
Sequence in context: A172454 A162001 A171713 * A174858 A246704 A095183
KEYWORD
nonn,base
AUTHOR
James S. DeArmon, Aug 11 2024
STATUS
approved