

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
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OFFSET

1,1


COMMENTS

In the GaussKuzmin distribution, 1 appears with probability lg 4/3 = 41.5037...%. Thus the nth appearance of 1 in the continued fraction of a real number chosen uniformly from [0, 1) will be, with probability 1, n / (lg 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



