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A178421 Lower primes p1 in a twin pair such that sum of p1 and p2 yields average a1 of twin prime pairs and product of 2*a1 is another average of twin prime pairs. 4
211049, 248639, 253679, 410339, 507359, 605639, 1121189, 1138829, 1262099, 2162579, 2172869, 2277659, 4070219, 6305459, 7671509, 11659409, 12577109, 14203769, 14862119, 17472839, 18728639, 18798359, 20520569, 21140699 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

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.

LINKS

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

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

Cf. A001097, A014574, A069142, A099349.

Sequence in context: A216593 A172825 A072760 * A069175 A097021 A236086

Adjacent sequences:  A178418 A178419 A178420 * A178422 A178423 A178424

KEYWORD

nonn

AUTHOR

Vladimir Joseph Stephan Orlovsky, May 27 2010

STATUS

approved

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Last modified August 14 06:43 EDT 2020. Contains 336477 sequences. (Running on oeis4.)