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A203168 Positions of 1 in the continued fraction expansion of Pi. 1
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 (list; graph; refs; listen; history; text; internal format)
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,changed

AUTHOR

Ben Branman, Dec 29 2011

STATUS

approved

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Last modified December 7 05:14 EST 2019. Contains 329839 sequences. (Running on oeis4.)