A076303 Engel expansion of exp(Pi * sqrt(163)) - 262537412640768743.

2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 6, 19, 1169, 21384, 520409, 2559029, 2922819, 3228884, 6972029, 18244654, 24601850, 146539491, 620041946, 865572355, 1298955860, 3005000777, 5169423076, 6941400197, 9965578146, 26183561695, 39614218376

Offset: 1

Author

Robert G. Wilson v, Mar 03 2003

Keywords

• nonn

Comments

262537412640768743.9999999999992500... is Ramanujan's constant which is extremely close to an integer. The Engel expansion of the fractional part begins with 40 terms 2.

Links

• OEIS wiki: Ramanujan's constant

Crossrefs

Cf. A006784, A060295.

Programs

Mathematica

EngelExp[ A_, n_ ] := Join[ Array[ 1 &, Floor[ A ]], First@ Transpose @ NestList[ {Ceiling[ 1/Expand[ #[[ 1 ]] #[[ 2 ]] - 1 ]], Expand[ #[[ 1 ]] #[[ 2 ]] - 1]} &, {Ceiling[ 1/(A - Floor[A]) ], A - Floor[A]}, n - 1 ]]; EngelExp[E^(Pi*Sqrt[163]) - 262537412640768743, 52]

PARI

default(realprecision, 100000); r=exp(Pi*sqrt(163))-262537412640768743; for(i=1, 100, s=r*ceil(1/r)-1; print1(ceil(1/r), ", "); r=s); /* Georg Fischer, Nov 21 2020 */

Extensions

More terms from Georg Fischer, Nov 21 2020