OFFSET
1,1
COMMENTS
The definition means that a1/2, a1 and 2*a1 are all in A014574 (twin prime averages). - R. J. Mathar, Nov 02 2023
LINKS
Amiram Eldar, Table of n, a(n) for n = 1..10000
FORMULA
a(n) = A069175(n)-1. - R. J. Mathar, Nov 02 2023
EXAMPLE
211049 is a term since 211049 and 211051 are twin primes; 211049 + 211051 = 422100 is an average of twin primes, and 2*422100 = 844200 is another average of twin primes.
MATHEMATICA
lst={}; Do[p1=Prime[n]; p2=Prime[n+1]; a1=p1+p2; a2=2*a1; If[p2-p1==2&&PrimeQ[a1-1]&&PrimeQ[a1+1]&&PrimeQ[a2-1]&&PrimeQ[a2+1], AppendTo[lst, p1]], {n, 10!}]; lst
atpQ[{a_, b_}]:=Module[{m=a+b}, b-a==2&&AllTrue[m+{1, -1}, PrimeQ] && AllTrue[ 2m+{1, -1}, PrimeQ]]; Select[Partition[Prime[Range[134*10^4]], 2, 1], atpQ][[All, 1]] (* Requires Mathematica version 10 or later *) (* Harvey P. Dale, Aug 28 2019 *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Vladimir Joseph Stephan Orlovsky, May 27 2010
STATUS
approved