A375091 First element p of sexy prime pairs (p,p+6) whose concatenation is also prime.

11, 13, 17, 31, 83, 97, 101, 151, 157, 167, 223, 227, 233, 251, 257, 263, 271, 331, 353, 373, 433, 461, 541, 601, 653, 677, 727, 821, 823, 877, 941, 971, 1013, 1033, 1181, 1187, 1223, 1367, 1447, 1453, 1657, 1693, 1741, 1861, 1973, 1993, 1997, 2207, 2281, 2333, 2393, 2441

Offset

1,1

Links

Table of n, a(n) for n=1..52.

Example

11 is the first term, since (11,17) are sexy primes and 1117 is also prime.
The second term is 13, since 1319 is prime.

Maple

q:= p-> andmap(isprime, [p, p+6, parse(cat(p, p+6))]):
select(q, [$2..3000])[];  # Alois P. Heinz, Aug 02 2024

Mathematica

Select[Prime[Range[370]], PrimeQ[#+6] && PrimeQ[FromDigits[Join[IntegerDigits[#], IntegerDigits[#+6]]]] &] (* Stefano Spezia, Aug 03 2024 *)

Prog

(Python)
from sympy import isprime
def ok(n): return isprime(n) and isprime(n+6) and isprime(int(str(n)+str(n+6)))
print([k for k in range(2500) if ok(k)]) # Michael S. Branicky, Aug 01 2024
(PARI) isp(p) = isprime(p+6) && isprime(eval(concat(Str(p), Str(p+6))))
select(isp, primes(100)) \\ Michel Marcus, Aug 02 2024

Crossrefs

Intersection of A023201 and A032621.

Cf. A031924, A104227, A032629.

Sequence in context: A090236 A240623 A240624 * A032502 A209871 A347702

Adjacent sequences: A375088 A375089 A375090 * A375092 A375093 A375094

Keyword

nonn,base

Author

James S. DeArmon, Jul 29 2024

Status

approved