A153408 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.

4831, 9013, 13859, 33809, 35051, 48353, 51593, 52177, 61333, 62219, 77761, 95131, 102643, 105167, 105691, 109717, 111779, 114799, 119771, 128239, 135391, 136739, 138727, 149239, 153991, 159793, 163223, 165449, 174859, 188687, 195991, 208049

Offset: 1

Author

Vladimir Joseph Stephan Orlovsky, Dec 25 2008

Keywords

• nonn

Examples

			4813*4817*4831 + 4 + 14 = 112002971670 and 112002971670 +- 1 are primes.
		

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A099349, A153374, A153375, A153376, A153377, A153378, A153379, A153402, A153404, A153405, A153406, A153407.

Programs

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

Mathematica

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
Select[Partition[Prime[Range[20000]],3,1],AllTrue[Times@@#+Total[ Differences[ #]]+ {2,0},PrimeQ]&][[All,3]] (* Harvey P. Dale, Apr 22 2022 *)

Extensions

Definition modified by Harvey P. Dale, Apr 22 2022