A071940 - OEIS

%I #19 Aug 04 2024 13:36:45

%S 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,

%T 12,12,12,12,13,13,13,13,13,13,14,15,15,15,16,16,17,17,17,17,18,18,19,

%U 20,20,21,22,23,23,24,25,25,26,27,27,28,28,29,30,30,30,30,30,31,31,31,31

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

%e 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.

%t Accumulate[If[#>1,0,1]&/@ContinuedFraction[Pi,100]] (* _Harvey P. Dale_, Feb 27 2023 *)

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

%Y Cf. A001203.

%K easy,nonn

%O 1,6

%A _Benoit Cloitre_, Jun 15 2002