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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 (list; constant; graph; refs; listen; history; text; internal format)
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 A247036 A202320

Adjacent sequences:  A039659 A039660 A039661 * A039663 A039664 A039665

KEYWORD

nonn,more,cons

AUTHOR

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

STATUS

approved

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Last modified November 24 04:08 EST 2014. Contains 249867 sequences.