A236302 Primes p such that p+8, p+86, p+864 are prime.

23, 743, 983, 1163, 1373, 1613, 2663, 4013, 4643, 6113, 6863, 7583, 7673, 8513, 10313, 10853, 11243, 12503, 12713, 15233, 15263, 25733, 25763, 28703, 39623, 40763, 42743, 46133, 54623, 56093, 61643, 63353, 65003, 67733, 68813, 70373, 70913, 71933, 78893, 86453

Offset: 1

Author

K. D. Bajpai, Apr 21 2014

Keywords

• nonn

Comments

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

The constants in the definition (8, 86 and 864) are the concatenation of successive even digits 8,6 and 4.

Examples

			a(1) = 23 is a prime: 23+8 = 31, 23+86 = 109 and 23+864 = 887 are also prime.
a(2) = 743 is a prime: 743+8 = 751, 743+86 = 829 and 743+864 = 1607 are also prime.
		

Links

• K. D. Bajpai, Table of n, a(n) for n = 1..4796

Crossrefs

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

Programs

Maple

KD:= proc() local a,b,d,e,f; a:= ithprime(n); b:=a+8;d:=a+86;e:=a+864; 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 + 8] && PrimeQ[p + 86] && PrimeQ[p + 864],AppendTo[KD, p]], {n, 15000}]; KD
c=0; p=Prime[n]; Do[If[PrimeQ[p+8]&&PrimeQ[p+86]&&PrimeQ[p+864],c=c+1;Print[c,"  ",p]], {n,1,5*10^6}]; (*b-file*)

PARI

s=[]; forprime(p=2, 90000, if(isprime(p+8) && isprime(p+86) && isprime(p+864), s=concat(s, p))); s \\ Colin Barker, Apr 21 2014