

A039662


Decimal expansion of Michael Trott's constant: continued fraction expansion (allowing 0's) begins in same way as decimal expansion.


6



1, 0, 8, 4, 1, 0, 1, 5, 1, 2, 2, 3, 1, 1, 1, 3, 6, 1, 5, 1, 1, 2, 9, 0, 8, 1, 1, 4, 0, 6, 4, 1, 5, 0, 9, 1, 1, 2, 2, 1, 5, 8, 0, 9, 0, 9, 3, 9, 0, 9, 0, 9, 1
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OFFSET

0,3


COMMENTS

I do not know if this can be modified to give more terms of agreement  N. J. A. Sloane.


LINKS

Table of n, a(n) for n=0..52.
Simon Plouffe, The Trott constant
The Mathematica Journal, Trott Constant
The Mathematica Journal, Trott's Corner, Finding Trott Constants
Eric Weisstein's World of Mathematics, Trott's constant


EXAMPLE

Let {a,b,c,d,...} mean a+1/(b+1/(c+1/(d+...))). Then {0,1,0,...,9,0,9,1} =
0 + 1/(1 + 1/(0 + 1/ (8 + 1/ (4 + 1/ (1 + 1/ (0 + 1/ (1 + 1/ (5 + 1/
(1 + 1/ (2 + 1/ (2 + 1/ (3 + 1/ (1 + 1/(1 + 1/(1 + 1/(3 + 1/(6 + 1/
(1 + 1/(5 + 1/(1 + 1/(1 + 1/(2 + 1/(9 + 1/(0 +1/(8 + 1/(1 + 1/(1 +
1/(4 + 1/(0 + 1/(6 + 1/(4 + 1/(1 + 1/(5 + 1/(0 + 1/(9 +1/(1 + 1/
(1 + 1/(2 + 1/(2 + 1/(1 + 1/(5 + 1/(8 + 1/(0 + 1/(9 + 1/(0 +
1/(9 + 1/(3 + 1/(9 + 1/(0 + 1/(9 + 1/1)))))
))))))))))))))))))))))))))))))))))))))))))))) =
17928273845270692 / 165374493467625219 = 0.108410151223111361511290811406414793...
and the digits agree to 32 places.


CROSSREFS

Cf. A039663, A091694, A113307, A114376, A169670.
Sequence in context: A199285 A049255 A028577 * A228496 A202320 A011267
Adjacent sequences: A039659 A039660 A039661 * A039663 A039664 A039665


KEYWORD

nonn,more,cons


AUTHOR

Simon Plouffe, Michael Trott (mtrott(AT)wolfram.com)


STATUS

approved



