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%I #14 Oct 27 2018 13:23:23
%S 109,137,191,197,283,521,617,683,907,991,1033,1117,1319,1493,1619,
%T 1627,1697,1741,1747,1801,1931,1949,2011,2111,2143,2153,2293,2417,
%U 2539,2543,2549,2591,2621,2837,2927,2953,2969,3079,3119,3187,3203,3329,3389,3407
%N Members of A164368 which are not Ramanujan primes.
%C Every lesser of twin primes (A001359), beginning with 137, which is not in A104272, is in the sequence. [From _Vladimir Shevelev_, Aug 31 2009]
%H J. Sondow, J. W. Nicholson, and T. D. Noe, <a href="http://arxiv.org/abs/1105.2249"> Ramanujan Primes: Bounds, Runs, Twins, and Gaps</a>, arXiv:1105.2249 [math.NT], 2011; J. Integer Seq. 14 (2011) Article 11.6.2.
%H V. Shevelev, <a href="http://arXiv.org/abs/0908.2319">On critical small intervals containing primes</a>, arXiv:0908.2319 [math.NT], 2009.
%H V. Shevelev, <a href="https://cs.uwaterloo.ca/journals/JIS/VOL15/Shevelev/shevelev19.html">Ramanujan and Labos Primes, Their Generalizations, and Classifications of Primes</a>, J. Int. Seq. 15 (2012) # 12.5.4.
%F A164368 \ A104272.
%e p=137 is the least lesser of twin primes which is not a Ramanujan prime. Therefore it is in the sequence. [From _Vladimir Shevelev_, Aug 31 2009]
%t nn = 250;
%t A164368 = Select[Prime[Range[2 nn]], PrimePi[2 NextPrime[#/2]] != PrimePi[#]&];
%t Rama = Table[0, {nn}]; s = 0; Do[If[PrimeQ[k], s++]; If[PrimeQ[k/2], s--]; If[s < nn, Rama[[s+1]] = k], {k, Prime[3 nn]}];
%t A104272 = Rama+1;
%t Complement[A164368, A104272] (* _Jean-François Alcover_, Oct 27 2018, after _T. D. Noe_ in A104272 *)
%Y Cf. A104272, A001262, A001567, A062568, A141232.
%K nonn
%O 1,1
%A _Vladimir Shevelev_, Aug 12 2009
%E I added 521. - _Vladimir Shevelev_, Aug 17 2009
%E Redefined in terms of A164368 and extended by _R. J. Mathar_, Aug 18 2009
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