cp's OEIS Frontend

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

%I A375091 #36 Aug 03 2024 17:01:36
%S A375091 11,13,17,31,83,97,101,151,157,167,223,227,233,251,257,263,271,331,
%T A375091 353,373,433,461,541,601,653,677,727,821,823,877,941,971,1013,1033,
%U A375091 1181,1187,1223,1367,1447,1453,1657,1693,1741,1861,1973,1993,1997,2207,2281,2333,2393,2441
%N A375091 First element p of sexy prime pairs (p,p+6) whose concatenation is also prime.
%e A375091 11 is the first term, since (11,17) are sexy primes and 1117 is also prime.
%e A375091 The second term is 13, since 1319 is prime.
%p A375091 q:= p-> andmap(isprime, [p, p+6, parse(cat(p, p+6))]):
%p A375091 select(q, [$2..3000])[];  # _Alois P. Heinz_, Aug 02 2024
%t A375091 Select[Prime[Range[370]], PrimeQ[#+6] && PrimeQ[FromDigits[Join[IntegerDigits[#], IntegerDigits[#+6]]]] &] (* _Stefano Spezia_, Aug 03 2024 *)
%o A375091 (Python)
%o A375091 from sympy import isprime
%o A375091 def ok(n): return isprime(n) and isprime(n+6) and isprime(int(str(n)+str(n+6)))
%o A375091 print([k for k in range(2500) if ok(k)]) # _Michael S. Branicky_, Aug 01 2024
%o A375091 (PARI) isp(p) = isprime(p+6) && isprime(eval(concat(Str(p), Str(p+6))))
%o A375091 select(isp, primes(100)) \\ _Michel Marcus_, Aug 02 2024
%Y A375091 Intersection of A023201 and A032621.
%Y A375091 Cf. A031924, A104227, A032629.
%K A375091 nonn,base
%O A375091 1,1
%A A375091 _James S. DeArmon_, Jul 29 2024