A235871 Primes p such that p+2, p+24 and p+246 are also primes.

5, 17, 107, 617, 857, 1277, 1487, 2087, 3167, 3557, 4217, 6947, 7457, 7877, 10067, 12917, 13217, 14387, 15137, 17657, 20897, 21317, 22367, 22697, 27407, 27527, 27917, 28547, 29207, 29387, 30467, 31727, 32117, 33287, 33617, 35507, 36107, 47657, 49367, 49787

Offset: 1

Author

K. D. Bajpai, Apr 21 2014

Keywords

• nonn

Comments

All the terms in the sequence are congruent to 5 mod 6.

The constants in the definition (2, 24 and 246) are the concatenation of first even digits 2,4 and 6.

Examples

			a(2) = 17 is a prime: 17+2 = 19, 17+24 = 41 and 17+246 = 263 are also prime.
a(3) = 107 is a prime: 107+2 = 119, 107+24 = 131 and 107+246 = 353 are also prime.
		

Links

• K. D. Bajpai, Table of n, a(n) for n = 1..5178

Crossrefs

Cf. A000040, A023200, A046136, A230223, A237890.

Programs

Maple

KD:= proc() local a,b,d,e; a:= ithprime(n); b:=a+2;d:=a+24;e:=a+246; if isprime(b) and isprime(d) and isprime(e) then return (a) :fi; end: seq(KD(), n=1..15000);

Mathematica

KD = {}; Do[p = Prime[n]; If[PrimeQ[p + 2] && PrimeQ[p + 24] && PrimeQ[p + 246], AppendTo[KD, p]], {n, 15000}]; KD
c = 0; p = Prime[n]; Do[If[PrimeQ[p + 2] && PrimeQ[p + 24] && PrimeQ[p + 246], c = c + 1; Print[c, " ", Prime[n]]], {n, 1, 5000000}];  (* b - file *)

PARI

s=[]; forprime(p=2, 50000, if(isprime(p+2) && isprime(p+24) && isprime(p+246), s=concat(s, p))); s \\ Colin Barker, Apr 21 2014