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%I #16 Apr 25 2015 11:46:00
%S 0,1,2,3,4,6,8,11,12,15,16,20,21,22,25,26,30,31,34,38,46,48,51,58,63,
%T 66,68,71,73,90,91,92,95,98,113,114,116,118,121,128,136,142,143,144,
%U 146,158,161,164,165,178,180,185,188,191,198,208,214,216,222,225,231,232,234,236,238,248,252,256,260,264,283,288,295,298,301,303,310,311,330,333
%N Numbers m with 9*m + 3*r - 1 and 9*m + 3*r + 1 twin prime for some r = 0,1,2.
%C By the conjecture in A257317, any positive integer should be the sum of two distinct terms of the current sequence one of which is even.
%H Zhi-Wei Sun, <a href="/A257121/b257121.txt">Table of n, a(n) for n = 1..10000</a>
%H Zhi-Wei Sun, <a href="http://arxiv.org/abs/1504.01608">Natural numbers represented by floor(x^2/a) + floor(y^2/b) + floor(z^2/c)</a>, arXiv:1504.01608 [math.NT], 2015.
%e a(1) = 0 since {9*0+3*2-1,9*0+3*2+1} = {5,7} is a twin prime pair.
%e a(2) = 1 since {9*1+3*1-1,9*1+3*1+1} = {11,13} is a twin prime pair.
%e a(3) = 2 since {9*2+3*0-1,9*2+3*0+1} = {17,19} is a twin prime pair.
%t TQ[m_]:=PrimeQ[3m-1]&&PrimeQ[3m+1]
%t PQ[m_]:=TQ[3*m]||TQ[3*m+1]||TQ[3*m+2]
%t n=0;Do[If[PQ[m],n=n+1;Print[n," ",m]],{m,0,340}]
%Y Cf. A014574, A256707, A257317.
%K nonn
%O 1,3
%A _Zhi-Wei Sun_, Apr 25 2015
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