A071113 Numbers k such that the number of terms in the continued fraction for (1 + 1/x)^x equals k for some x.

1, 2, 5, 7, 10, 14, 16, 20, 24, 29, 39, 40, 42, 44, 46, 55, 57, 59, 66, 68, 70, 81, 86, 91, 106, 108, 109, 117, 118, 119, 120, 123, 124, 133, 142, 147, 155, 159, 163, 164, 167, 168, 171, 176, 177, 198, 201, 205, 206, 213, 217, 226, 227, 228, 229, 233, 238, 246

Offset

1,2

Comments

It appears that lim_{n -> infinity} a(n)/(n*log(n)) = 1. - Benoit Cloitre, Jan 29 2006

Links

Table of n, a(n) for n=1..58.

Prog

(PARI) for(n=1, 300, if(sum(i=1, n, if(length(contfrac((1+1/i)^i))-n, 0, 1))>0, print1(n, ", ")))

Crossrefs

Sequence in context: A241510 A088947 A288209 * A071704 A267374 A267379

Adjacent sequences: A071110 A071111 A071112 * A071114 A071115 A071116

Keyword

easy,nonn

Author

Benoit Cloitre, May 27 2002

Status

approved