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

1,1

Links

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

Example

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

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 *)

Prog

(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

Crossrefs

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

Sequence in context: A252019 A372259 A299206 * A281885 A183589 A185990

Adjacent sequences: A153405 A153406 A153407 * A153409 A153410 A153411

Keyword

nonn

Author

Vladimir Joseph Stephan Orlovsky, Dec 25 2008

Extensions

Definition modified by Harvey P. Dale, Apr 22 2022

Status

approved