A153402 - OEIS

A153402

Smaller of 3 consecutive prime numbers such that p1*p2*p3+d1+d2-1=average of twin prime pairs, d1(delta)=p2-p1,d2(delta)=p3-p2.

%I #6 Jul 01 2018 15:21:49

%S 3,569,1747,5107,6947,9281,11027,14389,24851,25169,26189,31153,34469,

%T 41687,42391,45281,61091,62507,80603,82139,89989,91967,92333,93809,

%U 98369,98873,103583,105899,111347,117127,120977,122819,128411,135601

%N Smaller of 3 consecutive prime numbers such that p1*p2*p3+d1+d2-1=average of twin prime pairs, d1(delta)=p2-p1,d2(delta)=p3-p2.

%C 3*5*7+2+2-1=108+-1=prime,

%H Harvey P. Dale, <a href="/A153402/b153402.txt">Table of n, a(n) for n = 1..1000</a>

%t lst={};Do[p1=Prime[n];p2=Prime[n+1];p3=Prime[n+2];d1=p2-p1;d2=p3-p2;a=p1*p2*p3+d1+d2-1;If[PrimeQ[a-1]&&PrimeQ[a+1],AppendTo[lst,p1]],{n,8!}];lst

%t s3cpQ[{a_,b_,c_}]:=Module[{tp=a*b*c+(c-a)-1},AllTrue[tp+{1,-1},PrimeQ]]; Select[ Partition[Prime[Range[15000]],3,1],s3cpQ][[All,1]] (* The program uses the AllTrue function from Mathematica version 10 *) (* _Harvey P. Dale_, Jul 01 2018 *)

%Y Cf. A099349, A153374, A153375, A153376, A153377, A153378, A153379

%K nonn

%O 1,1

%A _Vladimir Joseph Stephan Orlovsky_, Dec 25 2008