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

1,1

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.

Links

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

Example

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.

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}];

Prog

(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

Crossrefs

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

Sequence in context: A339917 A174343 A158332 * A180531 A271926 A090258

Adjacent sequences: A241483 A241484 A241485 * A241487 A241488 A241489

Keyword

nonn

Author

K. D. Bajpai, Apr 23 2014

Status

approved