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A286195 Products of two numbers that are the average of a pair of twin primes.

%I A286195 #37 Jun 23 2017 08:19:08
%S A286195 16,24,36,48,72,108,120,144,168,180,216,240,252,288,324,360,408,432,
%T A286195 504,540,552,600,612,648,720,756,768,792,828,864,900,912,960,1080,
%U A286195 1128,1152,1188,1224,1248,1260,1296,1368,1392,1440,1620,1656,1680,1692,1728,1764,1800
%N A286195 Products of two numbers that are the average of a pair of twin primes.
%C A286195 Product of two numbers from A014574 in at least one way. - _David A. Corneth_, Jun 12 2017
%C A286195 For n > 1, a(n) is divisible by 12. All terms not in 4*A014574 are divisible by 36. - _Robert Israel_, Jun 12 2017
%C A286195 A075369 Union A288639.
%H A286195 Vincenzo Librandi and David A. Corneth, <a href="/A286195/b286195.txt">Table of n, a(n) for n = 1..10000 (first 1182 terms from Vincenzo Librandi)</a>
%e A286195 4 and 12 are the average of twin prime pairs (i.e., 4 = (3+5)/2 and 12 = (11+13)/2) and 4*12 = 48, which is in the sequence.
%e A286195 As 4 is the average of a twin prime pair, 4*4 = 16 is also in the sequence. - _David A. Corneth_, Jun 12 2017
%p A286195 N:= 2000: # to get all terms <= N
%p A286195 P:= select(isprime, {seq(i,i=3..N/4+1,2)}):
%p A286195 B:= map(`+`,P,1) intersect map(`-`,P,1):
%p A286195 sort(convert(select(`<=`,{seq(seq(B[i]*B[j],j=1..i),i=1..nops(B))},N),list));
%p A286195 # _Robert Israel_, Jun 12 2017
%t A286195 With[{nn = 1800}, TakeWhile[Union@ Map[Times @@ # &, Tuples[#, {2}]], # <= nn &] &@ Map[Mean, Select[Partition[Prime@ Range@ PrimePi@ nn, 2, 1], Differences@ # == {2} &]]] (* _Michael De Vlieger_, Jun 12 2017 *)
%o A286195 (PARI) upto(n) = {my(l1=List(),l2=List(),p,q);
%o A286195 p=2; forprime(q=3, n, if(q-p==2, listput(l1,p+1)); p=q); for(i=1,#l1,for(j=i,#l1, if(l1[i]*l1[j]<=n, listput(l2, l1[i]*l1[j]), next(2)))); listsort(l2,1); l2} \\ prog adapted from PARI-prog from _Charles R Greathouse IV_ in A014574. - _David A. Corneth_, Jun 12 2017
%Y A286195 Cf. A014574, A249628, A288639.
%Y A286195 A075369 is a subsequence.
%K A286195 nonn
%O A286195 1,1
%A A286195 _Wesley Ivan Hurt_, Jun 12 2017