A153379 Larger of two consecutive prime numbers, p1 and p2 = p1 + d, such that p1*p2*d - d is the average of twin primes.

1193, 8923, 13997, 31847, 33113, 56039, 57593, 66593, 85843, 87803, 90583, 91229, 93503, 101323, 103183, 111697, 113123, 127453, 141403, 142897, 150373, 150413, 151673, 152623, 156823, 157133, 161983, 176849, 179743, 186013, 205963, 209431

Offset

1,1

Links

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

Example

1193 since 1187 and 1193 = 1187 + 6 are consecutive primes, 1187*1193*6 - 6 = 8496540, and (8496539, 8496541) are twin primes.

Mathematica

lst={}; Do[p1=Prime[n]; p2=Prime[n+1]; d=p2-p1; a=p1*p2*d-d; If[PrimeQ[a-1]&&PrimeQ[a+1], AppendTo[lst, p2]], {n, 8!}]; lst
l2cpQ[{a_, b_}]:=Module[{d=b-a}, AllTrue[a*b*d-d+{1, -1}, PrimeQ]]; Transpose[ Select[ Partition[Prime[Range[20000]], 2, 1], l2cpQ]][[2]] (* The program uses the AllTrue function from Mathematica version 10 *) (* Harvey P. Dale, Oct 18 2015 *)

Prog

(Magma) [q:p in PrimesUpTo(210000)| IsPrime(a-1) and IsPrime(a+1) where a is (p*q-1)*(q-p) where q is NextPrime(p)]; // Marius A. Burtea, Jan 03 2020

Crossrefs

Cf. A099349, A153374, A153375, A153376, A153377, A153378.

Sequence in context: A344628 A353263 A287049 * A103172 A251923 A251916

Adjacent sequences: A153376 A153377 A153378 * A153380 A153381 A153382

Keyword

nonn

Author

Vladimir Joseph Stephan Orlovsky, Dec 24 2008

Extensions

Name edited by Amiram Eldar, Jan 03 2020

Status

approved