A156785 - OEIS

%I #8 Jan 01 2019 19:52:03

%S 401,7187,39229,128257,149099,216179,347041,585889,767831,3574721,

%T 5171951,7407523,10186459,10626107,10866209,11192737,13645469

%N Primes that belong to A156781, A156782 and A156783.

%t q=9;lst={};Do[p0=Prime[n+0];p1=Prime[n+1];p2=Prime[n+2];p3=Prime[n+3];p4=Prime[n+4];If[PrimeQ[p0+p1+p2]&&PrimeQ[p2+p3+p4],AppendTo[lst,p2]],{n,q!}];a2=lst;lst={};Do[p0=Prime[n+0];p1=Prime[n+1];p2=Prime[n+2];p3=Prime[n+3];p4=Prime[n+4];p5=Prime[n+5];p6=Prime[n+6];p7=Prime[n+7];p8=Prime[n+8];If[PrimeQ[p0+p1+p2+p3+p4]&&PrimeQ[p4+p5+p6+p7+p8],AppendTo[lst,p4]],{n,q!}];a4=lst;lst={};Do[p0=Prime[n+0];p1=Prime[n+1];p2=Prime[n+2];p3=Prime[n+3];p4=Prime[n+4];p5=Prime[n+5];p6=Prime[n+6];p7=Prime[n+7];p8=Prime[n+8];p9=Prime[n+9];p10=Prime[n+10];p11=Prime[n+11];p12=Prime[n+12];If[PrimeQ[p0+p1+p2+p3+p4+p5+p6]&&PrimeQ[p6+p7+p8+p9+p10+p11+p12],AppendTo[lst,p6]],{n,q!}];a6=lst;Intersection[a2,a4,a6]

%t cpQ[n_]:=Module[{a=Total/@Table[Take[n,{i,7}],{i,1,5,2}],b=Total/@ Table[ Take[ n,{7,j}],{j,9,13,2}]},AllTrue[Flatten[{a,b}],PrimeQ]]; Select[Partition[ Prime[ Range[ 360000]],13,1],cpQ][[All,7]] (* The program uses the AllTrue function from Mathematica version 10 *) (* _Harvey P. Dale_, Jan 01 2019 *)

%Y Cf. A156781, A156782, A156783, A156784

%K nonn

%O 1,1

%A _Vladimir Joseph Stephan Orlovsky_, Feb 15 2009

%E More terms from _Harvey P. Dale_, Jan 01 2019