|
%I #18 Sep 08 2022 08:45:39
%S 4831,9013,13859,33809,35051,48353,51593,52177,61333,62219,77761,
%T 95131,102643,105167,105691,109717,111779,114799,119771,128239,135391,
%U 136739,138727,149239,153991,159793,163223,165449,174859,188687,195991,208049
%N Largest 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="/A153408/b153408.txt">Table of n, a(n) for n = 1..10000</a>
%e 4813*4817*4831 + 4 + 14 = 112002971670 and 112002971670 +- 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,p3]],{n,8!}];lst
%t Select[Partition[Prime[Range[20000]],3,1],AllTrue[Times@@#+Total[ Differences[ #]]+ {2,0},PrimeQ]&][[All,3]] (* _Harvey P. Dale_, Apr 22 2022 *)
%o (Magma) [NthPrime(k+2):k in [1..20000]| IsPrime(q-1) and IsPrime(q+1) where q is NthPrime(k)* NthPrime(k+1)* NthPrime(k+2)+ NthPrime(k+2)- NthPrime(k)+1]; // _Marius A. Burtea_, Dec 22 2019
%Y Cf. A099349, A153374, A153375, A153376, A153377, A153378, A153379, A153402, A153404, A153405, A153406, A153407.
%K nonn
%O 1,1
%A _Vladimir Joseph Stephan Orlovsky_, Dec 25 2008
%E Definition modified by _Harvey P. Dale_, Apr 22 2022
|
