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A153405 Larger 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 A153405 #18 Sep 08 2022 08:45:39
%S A153405 7,577,1759,5119,6959,9293,11057,14407,24877,25183,26209,31177,34483,
%T A153405 41729,42403,45293,61121,62539,80621,82153,90007,91997,92353,93827,
%U A153405 98387,98893,103613,105913,111409,117163,121001,122833,128431,135613
%N A153405 Larger 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 A153405 Amiram Eldar, <a href="/A153405/b153405.txt">Table of n, a(n) for n = 1..10000</a>
%e A153405 7 is a term since (3, 5, 7) are consecutive primes, 3*5*7 + 2 + 2 - 1 = 108, and 108 +-1 = are twin primes.
%t A153405 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, p3]], {n, 8!}]; lst (* _Vladimir Joseph Stephan Orlovsky_ *)
%t A153405 okQ[{a_, b_, c_}] := Module[{x = a b c + (b - a) + (c - b) - 1}, PrimeQ[x - 1] && PrimeQ[x + 1]]
%t A153405 Transpose[Select[Partition[Prime[Range[15000]], 3, 1], okQ]][[3]] (* _Harvey P. Dale_, Jan 18 2011 *)
%o A153405 (Magma) [p3:k in [1..14000]| IsPrime(p1*p2*p3+p3-p1-2) and IsPrime(p1*p2*p3+p3-p1) where p1 is NthPrime(k) where p2 is NthPrime(k+1) where p3 is NthPrime(k+2) ]; // _Marius A. Burtea_, Dec 31 2019
%Y A153405 Cf. A099349, A153374, A153375, A153376, A153377, A153378, A153379, A153402, A153404.
%K A153405 nonn
%O A153405 1,1
%A A153405 _Vladimir Joseph Stephan Orlovsky_, Dec 25 2008