A241486 Primes p such that p+4, p+444 and p+4444 are also prime.

13, 19, 79, 103, 229, 307, 643, 853, 859, 937, 1087, 1213, 1297, 1423, 1567, 1609, 1867, 2347, 2389, 2473, 3163, 3463, 3919, 4003, 4153, 4783, 4969, 5077, 5347, 5413, 5479, 5647, 5689, 5857, 6733, 6907, 6967, 7933, 8269, 9277, 9337, 9463, 10687, 10729, 11083

Offset: 1

Author

K. D. Bajpai, Apr 23 2014

Keywords

• nonn

Comments

All the terms in the sequence are congruent to 1 mod 6.

The constants in the definition (4, 444 and 4444) are the concatenations of the digit 4.

Examples

			a(1) = 13 is a prime: 13+4 = 17, 13+444 = 457 and 13+4444 = 4457 are also prime.
a(2) = 19 is a prime: 19+4 = 23, 19+444 = 463 and 19+4444 = 4463 are also prime.
		

Links

• K. D. Bajpai, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A000040, A023200, A046136, A230223, A236302, A236304, A237890, A241485.

Programs

Maple

KD:= proc() local a,b,d,e; a:= ithprime(n); b:=a+4; d:=a+444; e:=a+4444;if isprime(b)and isprime(d)and isprime(e)then return (a): fi;  end: seq(KD(), n=1..5000);

Mathematica

KD = {}; Do[p = Prime[n]; If[PrimeQ[p + 4] && PrimeQ[p + 444] && PrimeQ[p + 4444], AppendTo[KD, p]], {n, 5000}]; KD
(* For the b-file*) c = 0; p = Prime[n]; Do[If[PrimeQ[p + 4] && PrimeQ[p + 444] && PrimeQ[p + 4444], c = c + 1; Print[c, "  ", p]], {n, 1, 3*10^6}];

PARI

s=[]; forprime(p=2, 12000, if(isprime(p+4) && isprime(p+444) && isprime(p+4444), s=concat(s, p))); s \\ Colin Barker, Apr 25 2014