A241488 Primes p such that p+8, p+888 and p+8888 are also prime.

53, 263, 389, 431, 983, 1013, 1061, 1223, 1571, 1823, 2789, 3323, 3533, 3911, 4211, 5849, 6563, 6653, 7019, 7481, 8369, 8963, 9041, 9173, 9413, 9539, 9803, 10091, 10559, 10979, 12611, 12689, 12911, 13163, 13751, 13781, 14243, 14879, 15083, 16691, 17231, 17483

Offset: 1

Author

K. D. Bajpai, Apr 23 2014

Keywords

• nonn

Comments

All the terms in the sequence are congruent to 2 mod 3.

The constants in the definition (8, 888 and 8888) are the concatenation of digit 8.

Examples

			a(1) = 53 is a prime: 53+8 = 61, 53+888 = 941 and 53+8888 = 8941 are also prime.
a(2) = 263 is a prime: 263+8 = 271, 263+888 = 1151 and 263+8888 = 9151 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+8;d:=a+888;e:=a+8888; 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 + 8] && PrimeQ[p + 888] && PrimeQ[p + 8888], AppendTo[KD, p]], {n, 5000}]; KD
(*For the b-file*)  c = 0; p = Prime[n]; Do[If[PrimeQ[p + 8] && PrimeQ[p + 888] && PrimeQ[p + 8888], c = c + 1; Print[c, "  ", p]], {n, 1, 5*10^6}];
Select[Prime[Range[2500]],AllTrue[#+{8,888,8888},PrimeQ]&] (* The program uses the AllTrue function from Mathematica version 10 *) (* Harvey P. Dale, Jul 31 2017 *)

PARI

s=[]; forprime(p=2, 18000, if(isprime(p+8) && isprime(p+888) && isprime(p+8888), s=concat(s, p))); s \\ Colin Barker, Apr 25 2014