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%I #8 Jan 24 2015 11:11:36
%S 2,3,19,61,229,499,677,1009,1753,2089,2791,3167,10657,12379,12893,
%T 13477,15139,18553,20551,21871,25367,26227,26669,33601,36781,36931,
%U 41399,41413,43543,61543,63331,63839,68903,71993,75709,76343,76471,86629
%N Smallest of 3 consecutive prime numbers such that p1*p2*p3*d1*d2=average of twin prime pairs; p1,p2,p3 consecutive prime numbers; d1(delta)=p2-p1, d2(delta)=p3-p2.
%C 2*3*5*1*2=60+-1=primes, 3*5*7*2*2=420+-1=primes, 19*23*29*4*6=304152+-1=primes,...
%H Harvey P. Dale, <a href="/A153409/b153409.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;If[PrimeQ[a-1]&&PrimeQ[a+1],AppendTo[lst,p1]],{n,8!}];lst
%t cpnQ[{a_,b_,c_}]:=Module[{pr=a*b*c*(b-a)*(c-b)},AllTrue[pr+{1,-1}, PrimeQ]]; Transpose[Select[Partition[Prime[Range[10000]],3,1], cpnQ]][[1]] (* The program uses the AllTrue function from Mathematica version 10 *) (* _Harvey P. Dale_, Jan 24 2015 *)
%Y Cf. A099349, A153374, A153375, A153376, A153377, A153378, A153379, A153406, A153407, A153408
%K nonn
%O 1,1
%A _Vladimir Joseph Stephan Orlovsky_, Dec 25 2008
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