A153409 Smallest of 3 consecutive prime numbers such that p1*p2*p3*d1*d2=average of twin prime pairs; p1,p2,p3 consecutive prime numbers; d1(delta)=p2-p1, d2(delta)=p3-p2.

2, 3, 19, 61, 229, 499, 677, 1009, 1753, 2089, 2791, 3167, 10657, 12379, 12893, 13477, 15139, 18553, 20551, 21871, 25367, 26227, 26669, 33601, 36781, 36931, 41399, 41413, 43543, 61543, 63331, 63839, 68903, 71993, 75709, 76343, 76471, 86629

Offset

1,1

Comments

2*3*5*1*2=60+-1=primes, 3*5*7*2*2=420+-1=primes, 19*23*29*4*6=304152+-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; If[PrimeQ[a-1]&&PrimeQ[a+1], AppendTo[lst, p1]], {n, 8!}]; lst
cpnQ[{a_, b_, c_}]:=Module[{pr=a*b*c*(b-a)*(c-b)}, AllTrue[pr+{1, -1}, PrimeQ]]; Transpose[Select[Partition[Prime[Range[10000]], 3, 1], cpnQ]][[1]] (* The program uses the AllTrue function from Mathematica version 10 *) (* Harvey P. Dale, Jan 24 2015 *)

Crossrefs

Cf. A099349, A153374, A153375, A153376, A153377, A153378, A153379, A153406, A153407, A153408

Sequence in context: A171149 A157042 A128968 * A143893 A262957 A072263

Adjacent sequences: A153406 A153407 A153408 * A153410 A153411 A153412

Keyword

nonn

Author

Vladimir Joseph Stephan Orlovsky, Dec 25 2008

Status

approved