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

Author

James S. DeArmon, Jul 29 2024

Keywords

• nonn
• base

Examples

			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.
		

Crossrefs

Intersection of A023201 and A032621.

Cf. A031924, A104227, A032629.

Programs

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 *)

PARI

isp(p) = isprime(p+6) && isprime(eval(concat(Str(p), Str(p+6))))
select(isp, primes(100)) \\ Michel Marcus, Aug 02 2024

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