A081838 Let z(n) be the golden ratio truncated to n decimal digits; sequence gives n such that the last element in the continued fraction for z(n) is 2.

1, 2, 5, 7, 10, 13, 15, 25, 29, 30, 33, 34, 38, 39, 42, 43, 50, 52, 55, 59, 61, 67, 68, 69, 70, 72, 76, 77, 79, 80, 81, 85, 86, 87, 88, 89, 90, 94, 98, 99, 102, 104, 110, 121, 123, 124, 125, 126, 127, 128, 129, 130, 133, 135, 139, 146, 147, 148, 164, 166, 167, 175, 176

Offset

1,2

Links

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

Formula

It seems that a(n)/n -> C = 2.7...

Example

The continued fraction for (1+sqrt(5))/2 truncated to 10 decimal digits is z(10)=1.6180339887 = [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 5, 2, 1, 1, 4, 1, 10, 36, 2], hence 10 is in the sequence.

Crossrefs

Sequence in context: A344988 A255774 A364005 * A057347 A067008 A376959

Adjacent sequences: A081835 A081836 A081837 * A081839 A081840 A081841

Keyword

base,nonn

Author

Benoit Cloitre, Apr 11 2003

Status

approved