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

1,1

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.

Links

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

Example

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.

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*)

Prog

(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

Crossrefs

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

Sequence in context: A168487 A299057 A299818 * A075942 A253925 A196658

Adjacent sequences: A236301 A236302 A236303 * A236305 A236306 A236307

Keyword

nonn

Author

K. D. Bajpai, Apr 21 2014

Status

approved