A393968 Decimal expansion of Pi_5, a generalized version of Pi used in squigonometry.

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

Offset

1,1

Links

Paolo Xausa, Table of n, a(n) for n = 1..10000

Robert D. Poodiack, Squigonometry, Hyperellipses, and Supereggs, Mathematics Magazine, vol. 89, no. 2, 2016, pp. 92-102.

Wikipedia, Squigonometry.

Formula

Equals 2*Pi*sqrt(2 + 2/sqrt(5))*Gamma(6/5)/(Gamma(2/5)*Gamma(4/5)) (see Poodiack, 2016, eq. 8).

Equals 10*Gamma(6/5)^2/Gamma(2/5) = 10*A371856^2/A246745.

Equals 2*Integral_{t=0..1} 1/((1 - t^5)^(4/5)) dt.

Example

3.800600555953746966012230617684211958045940397113...

Mathematica

First[RealDigits[10*Gamma[6/5]^2/Gamma[2/5], 10, 100]] (* or *)
First[RealDigits[2*Integrate[1/((1 - t^5)^(4/5)), {t, 0, 1}], 10, 100]]

Crossrefs

Cf. A393967 (Pi_3), A175576 (Pi_4).

Cf. A246745, A371856.

Sequence in context: A103319 A341812 A374944 * A153021 A155979 A120669

Adjacent sequences: A393965 A393966 A393967 * A393969 A393970 A393971

Keyword

nonn,cons

Author

Paolo Xausa, Mar 25 2026

Status

approved