A236304 Primes p such that p+12, p+1234 and p+123456 are also prime.

127, 907, 3037, 3457, 5737, 7057, 11047, 15427, 15667, 21517, 24697, 30307, 38287, 38317, 39607, 40177, 46477, 47797, 48787, 51157, 52177, 57667, 65587, 70627, 70867, 71887, 72997, 74857, 75277, 80317, 99817, 100447, 103657, 106747, 128437, 130087, 132157

Offset: 1

Author

K. D. Bajpai, Apr 21 2014

Keywords

• nonn

Comments

All the terms in the sequence are congruent to 1 mod 3.

The constants in the definition (12, 1234 and 123456) are the concatenation of digits 1,2,3,4,5 and 6.

Examples

			a(1) = 127 is a prime: 127+12 = 139, 127+1234 = 1361 and 127+123456 = 123583 are also prime.
a(2) = 907 is a prime: 907+12 = 919, 907+1234 = 2141 and 907+123456 = 124363 are also prime.
		

Links

• K. D. Bajpai, Table of n, a(n) for n = 1..5077

Crossrefs

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

Programs

Maple

KD:= proc() local a,b,d,e; a:= ithprime(n); b:=a+12;d:=a+1234;e:=a+123456; 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+12]&&PrimeQ[p+1234]&&PrimeQ[p+123456], AppendTo[KD,p]], {n,15000}];KD
c=0; p=Prime[n]; Do[If[PrimeQ[p+12]&&PrimeQ[p+1234]&&PrimeQ[p+123456], c=c+1; Print[c,"  ",p]],{n,1,5*10^6}];(*b-file*)

PARI

s=[]; forprime(p=2, 140000, if(isprime(p+12) && isprime(p+1234) && isprime(p+123456), s=concat(s, p))); s \\ Colin Barker, Apr 22 2014