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

1,1

Links

Michael S. Branicky, Table of n, a(n) for n = 1..10000

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

Adjacent sequences: A375310 A375311 A375312 * A375314 A375315 A375316

Keyword

nonn,base

Author

James S. DeArmon, Aug 11 2024

Status

approved