

A071940


Number of 1's among the n first elements of the simple continued fraction for Pi.


0



0, 0, 0, 1, 1, 2, 3, 4, 4, 5, 5, 6, 6, 6, 7, 8, 8, 8, 8, 8, 9, 9, 9, 10, 11, 11, 11, 11, 12, 12, 12, 12, 12, 12, 13, 13, 13, 13, 13, 13, 14, 15, 15, 15, 16, 16, 17, 17, 17, 17, 18, 18, 19, 20, 20, 21, 22, 23, 23, 24, 25, 25, 26, 27, 27, 28, 28, 29, 30, 30, 30, 30, 30, 31, 31, 31, 31
(list;
graph;
refs;
listen;
history;
text;
internal format)



OFFSET

1,6


COMMENTS

a(100)/100 = 0,41 Does lim n >infinity a(n)/n = (Log(4)Log(3)) / Log(2) =0,415... the expected density of "1's" ? (cf. measure theory of continued fraction)


LINKS

Table of n, a(n) for n=1..77.


EXAMPLE

Continued fraction for Pi begins : 3, 7, 15, 1, 292, 1, 1,.... there are 3 "1's" among the 7 first terms, hence a(7)=3.


PROG

(PARI) for(n=1, 100, print1(sum(i=1, n, if(component(contfrac(Pi), i)1, 0, 1)), ", "))


CROSSREFS

Cf. A001203.
Sequence in context: A174697 A176504 A196162 * A085883 A265912 A094192
Adjacent sequences: A071937 A071938 A071939 * A071941 A071942 A071943


KEYWORD

easy,nonn,cofr


AUTHOR

Benoit Cloitre, Jun 15 2002


STATUS

approved



