A393089 Decimal expansion of log(2)/4 - Pi/24.

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

Offset

0,2

Comments

The summation formula listed in Shamos is wrong.

References

Konrad Knopp, Theory and application of infinite series, Blackie & Son Limited, London and Glasgow, 1954. See exercise 107 at page 268.

Links

Table of n, a(n) for n=0..100.

Michael I. Shamos, A catalog of the real numbers, (2007). See p. 77.

Formula

Equals Sum_{k>=0} 1/((4*k + 1)*(4*k + 2)*(4*k + 3)*(4*k + 4)).

Equals Sum_{n>=0} Gamma(4*n + 1)/Gamma(4*n + 5). - Artur Jasinski, Feb 22 2026

Example

0.0423871012404116090850312227278981885106596419494...

Mathematica

Join[{0}, RealDigits[Log[2]/4-Pi/24, 10, 100][[1]]]

Crossrefs

Cf. A054777.

Sequence in context: A201651 A357463 A349119 * A026246 A396057 A321122

Adjacent sequences: A393086 A393087 A393088 * A393090 A393091 A393092

Keyword

nonn,cons,easy

Author

Stefano Spezia, Feb 01 2026

Status

approved