A153406 Smallest 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.

4813, 9007, 13831, 33791, 35023, 48337, 51577, 52153, 61297, 62207, 77743, 95107, 102607, 105137, 105673, 109663, 111767, 114781, 119747, 128221, 135367, 136727, 138679, 149197, 153949, 159787, 163199, 165437, 174829, 188677, 195973, 208009

Offset

1,1

Comments

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

Links

Harvey P. Dale, Table of n, a(n) for n = 1..1000

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, p1]], {n, 8!}]; lst
s3cpnQ[n_]:=Module[{c=Times@@n+Total[Differences[n]]+1}, AllTrue[c+{1, -1}, PrimeQ]]; Transpose[Select[Partition[ Prime[Range[ 20000]], 3, 1], s3cpnQ]] [[1]] (* The program uses the AllTrue function from Mathematica version 10 *) (* Harvey P. Dale, Nov 05 2014 *)

Crossrefs

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

Sequence in context: A035786 A108010 A029553 * A153407 A339468 A252019

Adjacent sequences: A153403 A153404 A153405 * A153407 A153408 A153409

Keyword

nonn

Author

Vladimir Joseph Stephan Orlovsky, Dec 25 2008

Status

approved