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Middle 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.
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%I #7 Dec 22 2019 08:04:42

%S 5,571,1753,5113,6949,9283,11047,14401,24859,25171,26203,31159,34471,

%T 41719,42397,45289,61099,62533,80611,82141,90001,91969,92347,93811,

%U 98377,98887,103591,105907,111373,117133,120997,122827,128413,135607

%N Middle 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.

%H Amiram Eldar, <a href="/A153404/b153404.txt">Table of n, a(n) for n = 1..10000</a>

%e 3*5*7 + 2 + 2 - 1 = 108 and 108 +- 1 are primes.

%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,p2]],{n,8!}];lst

%Y Cf. A099349, A153374, A153375, A153376, A153377, A153378, A153379, A153402.

%K nonn

%O 1,1

%A _Vladimir Joseph Stephan Orlovsky_, Dec 25 2008