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Continued fraction for (e + 1)/3.
2

%I #25 Aug 07 2024 22:39:47

%S 1,4,5,1,1,1,20,1,1,2,1,1,32,1,1,3,1,5,4,1,5,5,1,1,56,1,1,6,1,1,68,1,

%T 1,7,1,5,8,1,5,9,1,1,92,1,1,10,1,1,104,1,1,11,1,5,12,1,5,13,1,1,128,1,

%U 1,14,1,1,140,1,1,15,1,5,16,1,5,17,1,1,164,1,1,18,1,1,176,1,1,19,1,5,20

%N Continued fraction for (e + 1)/3.

%H Harry J. Smith, <a href="/A028360/b028360.txt">Table of n, a(n) for n = 0..19999</a>

%H D. S. Thakur, <a href="https://doi.org/10.1006/jnth.1997.2134">Patterns of Continued Fractions for the Analogues of e and Related Numbers in the Function Field Case</a>, J. Number Theory, Vol. 66, pp. 129-147, 1997.

%H G. Xiao, <a href="http://wims.unice.fr/~wims/en_tool~number~contfrac.en.html">Contfrac</a>

%H <a href="/index/Con#confC">Index entries for continued fractions for constants</a>

%e 1.239427276153015078453429157... = 1 + 1/(4 + 1/(5 + 1/(1 + 1/(1 + ...)))). - _Harry J. Smith_, May 14 2009

%t ContinuedFraction[(E+1)/3,100] (* _Harvey P. Dale_, Sep 09 2017 *)

%o (PARI) { allocatemem(932245000); default(realprecision, 54000); x=contfrac((exp(1)+1)/3); for (n=1, 20000, write("b028360.txt", n-1, " ", x[n])); } \\ _Harry J. Smith_, May 14 2009

%Y Cf. A160388 (decimal expansion).

%K cofr,nonn

%O 0,2

%A _N. J. A. Sloane_

%E More terms from _James A. Sellers_

%E Offset changed by _Andrew Howroyd_, Aug 07 2024