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

Author

Benoit Cloitre, Jun 15 2002

Keywords

• easy
• nonn

Examples

			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.
		

Crossrefs

Cf. A001203.

Programs

Mathematica

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

PARI

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