A203168 Positions of 1 in the continued fraction expansion of Pi.

4, 6, 7, 8, 10, 12, 15, 16, 21, 24, 25, 29, 35, 41, 42, 45, 47, 51, 53, 54, 56, 57, 58, 60, 61, 63, 64, 66, 68, 69, 74, 79, 82, 84, 87, 89, 92, 94, 96, 98, 99, 104, 108, 113, 115, 116, 121, 125, 126, 134, 136, 138, 141, 144, 148, 149, 150, 154, 157, 158, 160

Offset

1,1

Comments

In the Gauss-Kuzmin distribution, 1 appears with probability log_2(4/3) = 41.5037...%. Thus the n-th appearance of 1 in the continued fraction of a real number chosen uniformly from [0, 1) will be, with probability 1, n / (log_2(4/3)) + O(sqrt(n)). Does this sequence have the same asymptotic? - Charles R Greathouse IV, Dec 30 2011

Links

T. D. Noe, Table of n, a(n) for n = 1..1000

Eric Weisstein's World of Mathematics, Pi Continued Fraction

Index entries for continued fractions for constants

Index entries for sequences related to the number Pi

Formula

A001203(a(n)) = 1.

Mathematica

Flatten[Position[ContinuedFraction[Pi, 160], 1]]

Prog

(PARI) v=contfrac(Pi); for(i=1, #v, if(v[i]==1, print1(i", "))) \\ Charles R Greathouse IV, Dec 30 2011

Crossrefs

Cf. A001203, A033089, A000796.

Sequence in context: A305415 A105432 A324704 * A284820 A284623 A139490

Adjacent sequences: A203165 A203166 A203167 * A203169 A203170 A203171

Keyword

nonn,nice

Author

Ben Branman, Dec 29 2011

Status

approved