This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A291153 #48 Oct 19 2017 13:33:25
%S A291153 3,5,9,15,26,51,91,160,290,526,959,1767,3279,6113,11426,21456,40448,
%T A291153 76548,145205,276032,526142,1004977,1924032,3689162,7086486,13633821,
%U A291153 26269617,50680636,97899691,189336057,366569494,710444878,1378224063,2676107406,5200648226,10114912373,19687771058,38348128843,74746149884,145785668141,284517554507,555594884599,1085551499862,2122142209034,4150687469435
%N A291153 a(n) is the prime index of A191304(n+1).
%C A291153 The left point (x,y) of intersection of quadratic fits of log(a(n)) and log(A191304(n+1)) is about (-1, 0).
%C A291153 a(n+1) < 2 a(n) for all n, and lim_{n->inf} a(n+1)/a(n) = 2.
%C A291153 With A167168(1)=3 and s_1 = {3,5,11,23,...}, p_(a(n)) = s_1(n+1) in a two-index notation for every prime p_i for i > 1 based on Shevelev's equivalence classes of Rowland-like prime sequence recurrences. These equivalence classes {s_n(k)} were defined by Shevelev, see Crossrefs.
%F A291153 a(n) = pi(A191304(n+1)).
%F A291153 (4/5)^2 (n - 1) < log(a(n)) < (4/5)^2 (n + 1), for at least n < 46.
%e A291153 p_(a(3)) = A000040(a(3)) = A000040(9) = 23 = s_1(3+1) with
%e A291153 s_1 = {3,5,11,23,...}.
%t A291153 Rest@ PrimePi@ Union@ FoldList[Max, 1, Rest@ # - Most@ #] &@ FoldList[#1 + GCD[#2, #1] &, 7, Range[2, 10^7]] (* after _Michael De Vlieger_, Aug 19 2017, after _Robert G. Wilson v_ at A132199 *)
%Y A291153 Cf. A191304, A167168 (equivalence classes), A000040 (prime numbers).
%K A291153 nonn
%O A291153 1,1
%A A291153 _Ralf Steiner_, Aug 19 2017