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A185145 Smallest average of twin prime pairs s such that n*s is also average of twin prime pairs.

%I A185145 #17 Jun 23 2017 18:31:26
%S A185145 4,6,4,18,6,12,6,30,12,6,18,6,150,30,4,12,6,4,12,12,42,30,6,18,6,12,4,
%T A185145 270,12,6,42,6,6,30,12,12,180,6,60,6,30,150,30,30,4,18,6,4,18,12,42,6,
%U A185145 150,30,12,60,4,6,18,4,462,180,1230,18,30,108,60,180,12
%N A185145 Smallest average of twin prime pairs s such that n*s is also average of twin prime pairs.
%C A185145 Probably for all n>1 and also for all average s there are at least an average n*s. Note that this is equivalent to the Twin Prime Conjecture. Verified n to 10^7. First consecutive averages: 4 to 34260.
%H A185145 G. C. Greubel, <a href="/A185145/b185145.txt">Table of n, a(n) for n = 1..5000</a>
%F A185145 a(n) = A014574(j) if n*A014574(j) = A014574(k).
%e A185145 A014574(12) = 150, then 13*150 = 1950 = A014574(60).
%t A185145 t=Select[Table[Prime[n] + 1, {n, 10^4}], PrimeQ[#1 + 1] & ]; Table[s:=t[[m]]; m=1; While[!PrimeQ[n*s-1] || !PrimeQ[n*s+1], m++]; s, {n,1,100}]
%Y A185145 Cf. A066388, A014574.
%K A185145 nonn
%O A185145 1,1
%A A185145 _Manuel Valdivia_, Mar 12 2012