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A142727 For definition see Comments lines.

%I A142727 #5 Jan 21 2014 12:30:21
%S A142727 1,2,3,4,6,6,8,8,9,12,12,14,15,16,16,18,20,20,22,24,24,24,25,27,30,30,
%T A142727 30,32,32,32,36,36,39,40,42,42,44,45,46,48,48,48,50,50,52,52,55,59,60,
%U A142727 60,60,60,60,64,64,66,66,67,69,70,71,72,75,76,76,78,80,81,84
%N A142727 For definition see Comments lines.
%C A142727 S is a sequence of numbers with repetitions, sorted in nondecreasing order.
%C A142727 Initially a(1) = 1 and S = N = {1,2,3,4,5,6,...}.
%C A142727 For each n >= 2, let p = prime(n), let a(n) = (p-1)st term of S and set S = S union a(n)*N. Repeat.
%C A142727 A sequence arising from one possible attempt to analyze A141586.
%H A142727 David Applegate, <a href="/A142727/b142727.txt">Table of n, a(n) for n = 1..1000</a>
%H A142727 David Applegate, <a href="/A142727/a142727.txt">Table of n, p(n), a(n), a(n)/n at intervals of 10000 up to 244190000</a>
%F A142727 A plot of the extended sequence suggests that a(n) ~= c n log(log(n)) + d n for constants c and d. For example, run: $ gnuplot> plot [] [1.27:1.35] a142727.txt using 1:4, 1.12+0.076*log(log(x)).
%e A142727 The first few stages in the calculation are as follows:
%e A142727 S = 1 2 3 4 5 6 7 8 9 10 11 12 13 14 ...
%e A142727 n = 2, p = 3, so a(2) is the 2nd term of S, which is 2.
%e A142727 Now S = 1 2 2 3 4 4 5 6 6 7 8 8 9 10 10 11 12 12 13 14 14 ...
%e A142727 n = 3, p = 5, so a(3) is the 4th term of S, which is 3.
%e A142727 Now S = 1 2 2 3 3 4 4 5 6 6 6 7 8 8 9 9 10 10 11 12 12 12 13 14 14 ...
%e A142727 n = 4, p = 7, so a(4) is the 6th term of S, which is 4.
%e A142727 Now S = 1 2 2 3 3 4 4 4 5 6 6 6 7 8 8 8 9 9 10 10 11 12 12 12 12 13 14 14 ...
%e A142727 n = 5, p = 11, so a(5) is the 10th term of S, which is 6.
%e A142727 And so on.
%K A142727 nonn
%O A142727 1,2
%A A142727 _David Applegate_ and _N. J. A. Sloane_, Oct 03 2008