A203168 - OEIS

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

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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