A142727 For definition see Comments lines.

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, 30, 32, 32, 32, 36, 36, 39, 40, 42, 42, 44, 45, 46, 48, 48, 48, 50, 50, 52, 52, 55, 59, 60, 60, 60, 60, 60, 64, 64, 66, 66, 67, 69, 70, 71, 72, 75, 76, 76, 78, 80, 81, 84

Offset: 1

Author

David Applegate and N. J. A. Sloane, Oct 03 2008

Keywords

• nonn

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.

Examples

			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.
		

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)).