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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

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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.

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)).

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

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 ...