A078737 Denominators of convergents to sqrt(e).

1, 1, 2, 3, 17, 20, 37, 353, 390, 743, 10049, 10792, 20841, 365089, 385930, 751019, 16157329, 16908348, 33065677, 843550273, 876615950, 1720166223, 50761436417, 52481602640, 103243039057, 3459501891521, 3562744930578, 7022246822099

Offset: 1

Author

Benoit Cloitre, Dec 20 2002

Keywords

• frac
• nonn

Crossrefs

Cf. A058281, A078736, A065919.

Programs

PARI

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

Formula

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