A153410 Middle of 3 consecutive prime numbers, p1, p2, p3, such that p1*p2*p3*d1*d2 = average of twin prime pairs; d1 (delta) = p2 - p1, d2 (delta) = p3 - p2.

3, 5, 23, 67, 233, 503, 683, 1013, 1759, 2099, 2797, 3169, 10663, 12391, 12899, 13487, 15149, 18583, 20563, 21881, 25373, 26237, 26681, 33613, 36787, 36943, 41411, 41443, 43573, 61547, 63337, 63841, 68909, 71999, 75721, 76367, 76481, 86677

Offset

1,1

Links

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

Example

2*3*5*1*2 = 60 and 60 +- 1 are primes.
3*5*7*2*2 = 420 and 420 +- 1 are primes.
19*23*29*4*6 = 304152 and 304152 +- 1 are primes.

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, p2]], {n, 8!}]; lst
cpnQ[{a_, b_, c_}]:=Module[{x=Times@@Join[{a, b, c}, Differences[ {a, b, c}]]}, AllTrue[ x+{1, -1}, PrimeQ]]; Select[Partition[ Prime[Range[ 10000]], 3, 1], cpnQ][[All, 2]] (* Requires Mathematica version 10 or later *) (* Harvey P. Dale, Aug 01 2020 *)

Crossrefs

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

Sequence in context: A023247 A027753 A066411 * A230080 A155778 A209028

Adjacent sequences: A153407 A153408 A153409 * A153411 A153412 A153413

Keyword

nonn

Author

Vladimir Joseph Stephan Orlovsky, Dec 25 2008

Status

approved