OFFSET
1,2
COMMENTS
S is a sequence of numbers with repetitions, sorted in nondecreasing order.
Initially a(1) = 1 and S = N = {1,2,3,4,5,6,...}.
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.
A sequence arising from one possible attempt to analyze A141586.
LINKS
David Applegate, Table of n, a(n) for n = 1..1000
David Applegate, Table of n, p(n), a(n), a(n)/n at intervals of 10000 up to 244190000
FORMULA
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)).
EXAMPLE
The first few stages in the calculation are as follows:
S = 1 2 3 4 5 6 7 8 9 10 11 12 13 14 ...
n = 2, p = 3, so a(2) is the 2nd term of S, which is 2.
Now S = 1 2 2 3 4 4 5 6 6 7 8 8 9 10 10 11 12 12 13 14 14 ...
n = 3, p = 5, so a(3) is the 4th term of S, which is 3.
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 ...
n = 4, p = 7, so a(4) is the 6th term of S, which is 4.
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 ...
n = 5, p = 11, so a(5) is the 10th term of S, which is 6.
And so on.
CROSSREFS
KEYWORD
nonn
AUTHOR
David Applegate and N. J. A. Sloane, Oct 03 2008
STATUS
approved