A153402 Smaller 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.

3, 569, 1747, 5107, 6947, 9281, 11027, 14389, 24851, 25169, 26189, 31153, 34469, 41687, 42391, 45281, 61091, 62507, 80603, 82139, 89989, 91967, 92333, 93809, 98369, 98873, 103583, 105899, 111347, 117127, 120977, 122819, 128411, 135601

Offset

1,1

Comments

3*5*7+2+2-1=108+-1=prime,

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
s3cpQ[{a_, b_, c_}]:=Module[{tp=a*b*c+(c-a)-1}, AllTrue[tp+{1, -1}, PrimeQ]]; Select[ Partition[Prime[Range[15000]], 3, 1], s3cpQ][[All, 1]] (* The program uses the AllTrue function from Mathematica version 10 *) (* Harvey P. Dale, Jul 01 2018 *)

Crossrefs

Cf. A099349, A153374, A153375, A153376, A153377, A153378, A153379

Sequence in context: A171359 A002306 A087574 * A121043 A058467 A137136

Adjacent sequences: A153399 A153400 A153401 * A153403 A153404 A153405

Keyword

nonn

Author

Vladimir Joseph Stephan Orlovsky, Dec 25 2008

Status

approved