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A088458

a(n) equals the number of partial quotients of the simple continued fraction expansion of the nonsimple continued fraction: 1/(1+2/(2+3/(3+...+n/n)))).

1, 2, 4, 6, 7, 8, 13, 11, 12, 18, 22, 20, 27, 27, 24, 32, 35, 34, 39, 43, 44, 42, 44, 53, 56, 54, 60, 67, 69, 59, 72, 75, 76, 72, 83, 81, 87, 81, 96, 99, 102, 107, 108, 106, 105, 112, 114, 115, 121, 130, 125, 129, 125, 131, 135, 152, 149, 139, 139, 150, 154, 161, 162

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OFFSET

1,2

COMMENTS

The finite nonsimple continued fraction, 1/(1+2/(2+3/(3+...+n/n)))), as n grows, has the limit: 1/(e-1) = [0;1,1,2,1,1,4,1,1,6,...] (A005131).

LINKS

Table of n, a(n) for n=1..63.

EXAMPLE

a(5)=7 since there are 7 partial quotients in the resultant simple continued fraction of 1/(1+2/(2+3/(3+4/(4+5/5)))) = 53/91 = [0;1,1,2,1,1,7].

The count of partial quotients includes the initial integer position.

CROSSREFS

Cf. A005131.