A153411 Larger 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.

5, 7, 29, 71, 239, 509, 691, 1019, 1777, 2111, 2801, 3181, 10667, 12401, 12907, 13499, 15161, 18587, 20593, 21893, 25391, 26249, 26683, 33617, 36791, 36947, 41413, 41453, 43577, 61553, 63347, 63853, 68917, 72019, 75731, 76369, 76487, 86689

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, p3]], {n, 8!}]; lst
tppQ[n_]:=Module[{c=Times@@Join[n, Differences[n]]}, AllTrue[c+{1, -1}, PrimeQ]]; Transpose[Select[Partition[Prime[Range[10^4]], 3, 1], tppQ]] [[3]] (* The program uses the AllTrue function from Mathematica version 10 *) (* Harvey P. Dale, Mar 17 2016 *)

Crossrefs

Cf. A099349, A153374, A153375, A153376, A153377, A153378, A153379, A153406, A153407, A153408, A153409, A153410

Sequence in context: A070153 A293943 A171619 * A081630 A307532 A135324

Adjacent sequences: A153408 A153409 A153410 * A153412 A153413 A153414

Keyword

nonn

Author

Vladimir Joseph Stephan Orlovsky, Dec 25 2008

Status

approved