A292817 b(0) = 1, b(2*n-1) = 1/(1+1^2/(1+1^2/(1+2^2/(1+2^2/(...+(n-1)^2/(1+n^2)))))) and b(2*n) = 1/(1+1^2/(1+1^2/(1+2^2/(1+2^2/(...+n^2/(1+n^2)))))). a(n) is the denominator of b(n).

1, 2, 3, 11, 23, 61, 329, 2281, 2515, 32285, 253195, 2577715, 11692735, 69000385, 78993865, 9542994065, 55043460305, 414012989785, 1057309252855, 17617828844255, 5873750196655, 1127553022142305, 17180305293984965, 341915575670968805

Offset

0,2

Comments

The limit of b(n) is (PolyGamma(1,(1+sqrt(5))/4)-PolyGamma(1,(3+sqrt(5))/4))/2. See A091659.

Links

Table of n, a(n) for n=0..23.

Eric Weisstein's World of Mathematics, Polygamma Function

Eric Weisstein's World of Mathematics, Ramanujan Continued Fractions

Example

b(0) = 1/1, so a(0) = 1.
b(1) = 1/(1+1^2) = 1/2, so a(1) = 2.
b(2) = 1/(1+1^2/(1+1^2)) = 2/3, so a(2) = 3.
b(3) = 1/(1+1^2/(1+1^2/(1+2^2))) = 6/11, so a(3) = 11.
b(4) = 1/(1+1^2/(1+1^2/(1+2^2/(1+2^2)))) = 14/23, so a(4) = 23.

Crossrefs

Cf. A091659, A292816.

Sequence in context: A119641 A252005 A074496 * A292112 A363141 A065849

Adjacent sequences: A292814 A292815 A292816 * A292818 A292819 A292820

Keyword

nonn,frac

Author

Seiichi Manyama, Sep 24 2017

Status

approved