A071940 Number of 1's among the first n terms of the simple continued fraction for Pi.

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

Offset

1,6

Links

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

Example

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

Mathematica

Accumulate[If[#>1, 0, 1]&/@ContinuedFraction[Pi, 100]] (* Harvey P. Dale, Feb 27 2023 *)

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 A356770 A265912

Adjacent sequences: A071937 A071938 A071939 * A071941 A071942 A071943

Keyword

easy,nonn,cofr

Author

Benoit Cloitre, Jun 15 2002

Status

approved