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%I #34 Nov 06 2016 01:56:32
%S 2,11,17,29,41,47,59,97,127,149,151,167,179,227,229,233,347,367,401,
%T 409,569,571,587,593,937,1423,1427,2237,2617,2657,2659,3251
%N Numbers R(k) such that R(k) >= 2k log R(k), where R(k) = A104272(k) is the k-th Ramanujan prime.
%C For all R(k) > 3251, or all k > 201, R(k) < 2k log R(k). - _John W. Nicholson_, Nov 05 2016
%H C. Axler, <a href="http://arxiv.org/abs/1401.7179">On generalized Ramanujan primes</a>, arXiv preprint arXiv:1401.7179 [math.NT], 2014.
%t nn = 201; R = Table[0, {nn}]; s = 0; Do[ If[ PrimeQ[k], s++]; If[ PrimeQ[k/2], s--]; If[s < nn, R[[s +1]] = k], {k, Prime[3nn]}]; R = R +1; R[[#]] & /@ Select[ Range@ nn, R[[#]] >= 2#*Log[R[[#]]] &] (* _Robert G. Wilson v_, Nov 05 2016 after _T. D. Noe_ in A104272 *)
%o (PARI)
%o \\With RR[i] a list of Ramanujan primes in A104272.
%o \\Program also gives the index i of A104272.
%o n=0;for(i=1,10^6,if(RR[i]/(2*i)>=log(RR[i]), print(n++," "i," ",primepi(RR[i])," ",RR[i])))
%K nonn,fini,full
%O 1,1
%A _John W. Nicholson_, Jan 03 2013
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