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%I #19 Mar 24 2017 00:47:52
%S 0,6,28,167,964,6305,45082,335919,2605867,20841010,170395131
%N Number of twin prime pairs < 10^n that contain at least one Ramanujan prime (A104272).
%C It appears that this gives the number of Ramanujan primes < 10^n that are the lesser prime in a twin prime pair. Equivalently, this sequence also gives the number of Ramanujan primes p with p+2 also prime less than 10^n.
%C It appears that no upper twin prime is a Ramanujan prime without the corresponding lower twin prime also being a Ramanujan prime.
%C This is proved in Section 4 of "Ramanujan Primes: Bounds, Runs, Twins, and Gaps".
%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>, J. Integer Seq. 14 (2011) Article 11.6.2.
%t nn=50000; t=Table[0,{nn}]; s=0; Do[If[PrimeQ[k], s++]; If[PrimeQ[k/2], s--]; If[s<nn, t[[s+1]]=k], {k, Prime[3*nn]}]; t=t+1; cnt=0; i=1; Table[While[t[[i]]<10^n, If[PrimeQ[t[[i]]+2], cnt++]; i++]; cnt, {n,Floor[Log[10,t[[-1]]]]}]
%Y Cf. A178128 (Ramanujan primes p such that p+2 is prime), A007508 (number of twin primes pairs < 10^n), A181678 (number of twin Ramanujan primes pairs < 10^n).
%K nonn,more
%O 1,2
%A _T. D. Noe_, Nov 22 2010
%E a(10)-a(11) from _Dana Jacobsen_, Apr 29 2015