%I #8 Apr 26 2014 11:04:47
%S 13,19,79,103,229,307,643,853,859,937,1087,1213,1297,1423,1567,1609,
%T 1867,2347,2389,2473,3163,3463,3919,4003,4153,4783,4969,5077,5347,
%U 5413,5479,5647,5689,5857,6733,6907,6967,7933,8269,9277,9337,9463,10687,10729,11083
%N Primes p such that p+4, p+444 and p+4444 are also prime.
%C All the terms in the sequence are congruent to 1 mod 6.
%C The constants in the definition (4, 444 and 4444) are the concatenations of the digit 4.
%H K. D. Bajpai, <a href="/A241486/b241486.txt">Table of n, a(n) for n = 1..10000</a>
%e a(1) = 13 is a prime: 13+4 = 17, 13+444 = 457 and 13+4444 = 4457 are also prime.
%e a(2) = 19 is a prime: 19+4 = 23, 19+444 = 463 and 19+4444 = 4463 are also prime.
%p 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);
%t KD = {}; Do[p = Prime[n]; If[PrimeQ[p + 4] && PrimeQ[p + 444] && PrimeQ[p + 4444], AppendTo[KD, p]], {n, 5000}]; KD
%t (* 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}];
%o (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
%Y Cf. A000040, A023200, A046136, A230223, A236302, A236304, A237890, A241485.
%K nonn
%O 1,1
%A _K. D. Bajpai_, Apr 23 2014