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%I #10 May 27 2021 09:33:06
%S 3,23,29,37,41,47,61,67,83,103,113,149,157,167,193,269,277,281,331,
%T 347,439,521,569,593,677,733,823,827,877,911,1019,1061,1097,1117,1153,
%U 1217,1259,1289,1381,1433,1447,1489,1499,1553,1607,1637,1693,1699,1733,1801
%N Primes of the form (p(n)+r(n))/3, where p(n) = n-th prime and r(n) = n-th nonprime.
%H Harvey P. Dale, <a href="/A142345/b142345.txt">Table of n, a(n) for n = 1..1000</a>
%e If n=3, then (p(3)+r(3))/3 = (5+4)/3 = 3 = a(1).
%e If n=15, then (p(15)+r(15))/3 = (47+22)/3 = 23 = a(2).
%e If n=18, then (p(18)+r(18))/3 = (61+26)/3 = 29 = a(3).
%e If n=22, then (p(22)+r(22))/3 = (79+32)/3 = 37 = a(4).
%e If n=24, then (p(24)+r(24))/3 = (89+34)/3 = 41 = a(5), etc.
%t Module[{nn=5000,pr,comp,len},pr=Prime[Range[PrimePi[nn]]];comp = Complement[ Range[0,nn],pr]; len = Min[ Length[pr],Length[comp]]; Select[Total[#]/3&/@Thread[ {Take[pr,len], Take[comp, len]}],PrimeQ]] (* _Harvey P. Dale_, Dec 04 2012 *)
%Y Cf. A000040, A141468.
%K nonn
%O 1,1
%A _Juri-Stepan Gerasimov_, Sep 19 2008
%E 167 inserted, 347 inserted and extended by _R. J. Mathar_, Nov 03 2008
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