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

1,1

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

Table of n, a(n) for n=1..61.

OEIS wiki: Ramanujan's constant

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]

Prog

(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 */

Crossrefs

Cf. A006784, A060295.

Sequence in context: A071702 A225541 A355480 * A339276 A343356 A242253

Adjacent sequences: A076300 A076301 A076302 * A076304 A076305 A076306

Keyword

nonn

Author

Robert G. Wilson v, Mar 03 2003

Extensions

More terms from Georg Fischer, Nov 21 2020

Status

approved