A078736 Numerators of convergents to sqrt(e).

1, 2, 3, 5, 28, 33, 61, 582, 643, 1225, 16568, 17793, 34361, 601930, 636291, 1238221, 26638932, 27877153, 54516085, 1390779278, 1445295363, 2836074641, 83691459952, 86527534593, 170218994545, 5703754354578, 5873973349123

Offset

1,2

Links

Table of n, a(n) for n=1..27.

Formula

Let y(n, x)=sum(k=0, n, (n+k)!*(x/2)^k/((n-k)!*k!)) then : a(3*n)=(1/2)*(y(n, 4)+y(n-1, 4)); a(3*n+1)=y(n, 4); a(3*n+2)=(1/2)*(y(n+1, 4)-y(n, 4))

Mathematica

Numerator[Convergents[Sqrt[E], 30]] (* Harvey P. Dale, Sep 23 2011 *)

Prog

(PARI) a(n)=component(component(contfracpnqn(contfrac(exp(1/2), n)), 1), 1)

Crossrefs

Cf. A058281, A078737, A065919.

Sequence in context: A121264 A141566 A247094 * A042669 A178376 A041585

Adjacent sequences: A078733 A078734 A078735 * A078737 A078738 A078739

Keyword

frac,nonn

Author

Benoit Cloitre, Dec 20 2002

Status

approved