A358463 - OEIS

%I #8 Nov 20 2022 11:07:55

%S 4,18,72,180,240,462,420,1062,660,1290,2142,2130,2550,2340,3822,6762,

%T 2310,3540,4788,6300,6360,5880,5280,6270,7350,8010,5850,15330,9240,

%U 10890,13398,7590,28548,19992,11970,22542,23688,11550,19140,20748,27060,18060,36930,25170,40152,29400,27690,25410

%N a(n) is the first average of a twin prime pair that is the sum of two distinct averages of twin prime pairs in exactly n ways.

%C a(n) is the first term of A014574 that is the sum of two distinct terms of A014574 in exactly n ways.

%H Robert Israel, <a href="/A358463/b358463.txt">Table of n, a(n) for n = 0..605</a>

%e a(3) = 180 because 180 is the average of twin primes 179 and 181, is the sum of two such averages in exactly 3 ways: 180 = 30 + 150 = 42 + 138 = 72 + 108, and no smaller average of twin primes works.

%p M:= select(t -> isprime(t+1) and isprime(t-1), {seq(i,i=6..10^6,6)}):V:= Vector(max(M)/6):for i from 2 to nops(M) do

%p   for j from 1 to i-1 do

%p     s:= M[i]+M[j];

%p     if s > 10^6 then break fi;

%p     if member(s,M) then

%p        V[s/6]:= V[s/6]+1;

%p     fi

%p od od:

%p A:= Array(0..100): A[0]:= 4:

%p for m in M do

%p   v:= V[m/6];

%p   if v <= 100 and A[v] = 0 then A[v]:= m fi

%p od:

%p convert(A,list);

%Y Cf. A014574.

%K nonn

%O 0,1

%A _J. M. Bergot_ and _Robert Israel_, Nov 17 2022