cp's OEIS Frontend

A191228 Greatest Ramanujan prime index less than x, eta(x).

%I A191228 #16 Nov 07 2018 03:55:27
%S A191228 0,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,4,4,4,4,4,4,
%T A191228 4,4,4,4,4,4,5,5,5,5,5,5,6,6,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,7,7,7,8,8,
%U A191228 8,8,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,10,10,10,10
%N A191228 Greatest Ramanujan prime index less than x, eta(x).
%C A191228 a(n) is the greatest value k of A104272(k) less than x. The integer inverse function of A104272.
%C A191228 Starting at index m = a(A174602(n)) in A190874(m), the first instance of a count of n - 1 consecutive 1's is seen.
%H A191228 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.
%e A191228 a(17) = eta(17) = 3. Or, R_3 = 17.
%t A191228 nn = 100; R = Table[0, {nn}]; s = 0;
%t A191228 Do[If[PrimeQ[k], s++]; If[PrimeQ[k/2], s--]; If[s < nn, R[[s + 1]] = k], {k, Prime[3 nn]}];
%t A191228 A104272 = R + 1;
%t A191228 Table[Boole[MemberQ[A104272, k]], {k, 1, 100}] // Accumulate (* _Jean-François Alcover_, Nov 07 2018, using _T. D. Noe_'s code for A104272 *)
%Y A191228 Cf. A104272, A191225, A191226, A191227.
%K A191228 nonn
%O A191228 1,11
%A A191228 _John W. Nicholson_, May 28 2011