A212131 Decimal expansion of k such that e^(k*sqrt(163)) = round(e^(Pi*sqrt(163))).

3, 1, 4, 1, 5, 9, 2, 6, 5, 3, 5, 8, 9, 7, 9, 3, 2, 3, 8, 4, 6, 2, 6, 4, 3, 3, 8, 3, 2, 7, 9, 7, 2, 6, 6, 1, 9, 3, 4, 7, 5, 4, 9, 8, 8, 0, 8, 8, 3, 5, 2, 2, 4, 2, 2, 2, 9, 2, 9, 6, 2, 8, 7, 7, 4, 4, 2, 2, 5, 8, 7, 3, 9, 0, 5, 1, 0, 4, 9, 3, 7, 8, 7, 5, 5, 1, 0, 7, 4, 4, 5, 7, 7, 6, 7, 2, 0, 2, 4, 1, 5, 7, 9, 6, 7

Offset: 1

Author

Omar E. Pol, Jun 25 2012

Keywords

• nonn
• cons

Comments

Decimal expansion of log(262537412640768744)/sqrt(163).

First differs from A000796 at a(32).

Note that 262537412640768744 = 24*10939058860032031 = 2^3 * 3 * 10939058860032031, is the nearest integer to the value of Ramanujan's constant e^(Pi*sqrt(163)) = 262537412640768743.999999999999250... = A060295.

Examples

			3.14159265358979323846264338327972661934754988... (very close to Pi).
		

Links

• Eric Weisstein's World of Mathematics, Ramanujan's constant

Crossrefs

Cf. A000796, A003173, A019297, A060295, A080283, A102912, A160514, A160515, A181045.

Programs

Mathematica

RealDigits[Log[Round[E^(Pi Sqrt[163])]]/Sqrt[163], 10, 105][[1]] (* Bruno Berselli, Jun 26 2012 *)

Formula

k = log(round(e^(Pi*sqrt(163))))/sqrt(163).

Extensions

More terms from Alois P. Heinz, Jun 25 2012