A387884 Decimal expansion of the Rogers-Ramanujan R(q) function evaluated at q = exp(-Pi).

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

Offset

0,1

Links

Paolo Xausa, Table of n, a(n) for n = 0..10000

Simon Plouffe, The numbers in the base e^Pi, 2025.

Wikipedia, Rogers-Ramanujan identities.

Formula

Equals (sqrt(5) + 1)*(sqrt(5) - s)*(5^(1/4) + s)/4, where s = sqrt(2 + sqrt(5)).

Equals q^(1/5)*Product_{k >= 0} (1 - q^(5*k + 1))*(1 - q^(5*k + 4))/((1 - q^(5*k + 2))*(1 - q^(5*k + 3))), where q = exp(-Pi).

Example

0.511428455403703519294633013542578810415754381417...

Mathematica

First[RealDigits[(Sqrt[5] + 1)*(Sqrt[5] - #)*(5^(1/4) + #)/4 & [Sqrt[2 + Sqrt[5]]], 10, 100]]

Crossrefs

Cf. A003106, A003114, A093580.

Sequence in context: A196612 A110635 A179773 * A244977 A071170 A332762

Adjacent sequences: A387881 A387882 A387883 * A387885 A387886 A387887

Keyword

nonn,cons,easy

Author

Paolo Xausa, Sep 17 2025

Status

approved