A241009 Decimal expansion of Sierpiński's S^ (Ŝ or "S hat" as named by S. Finch), a constant appearing in the asymptotics of the number of representations of a positive integer as a sum of two squares.

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

Offset

1,2

References

Steven R. Finch, Mathematical Constants, Cambridge University Press, 2003, Section 2.10 Sierpinski's constant, p. 122.

Links

Table of n, a(n) for n=1..101.

Steven R. Finch, Errata and Addenda to Mathematical Constants, Section 2.10 p. 17.

Formula

S_hat = gamma + S - 12/Pi^2*zeta'(2) + log(2)/3 - 1, where S = A086058 - 1 = A062089 / Pi.

Example

1.7710119609560939428739802335360529080166503945687208610228709...

Mathematica

S = 2* EulerGamma + 2*Log[2 ] + 3*Log[Pi] - 4* Log[Gamma[1/4]]; (* S^ *) Sh = EulerGamma + S - 12/Pi^2 Zeta'[2] + Log[2]/3 - 1; RealDigits[Sh, 10, 101] // First

Prog

(PARI) 3*Euler + 3*log(Pi) - 4*lngamma(1/4) - 12*zeta'(2)/Pi^2 + 7*log(2)/3 - 1 \\ Charles R Greathouse IV, Aug 08 2014

Crossrefs

Cf. A062089, A086058.

Sequence in context: A357102 A258149 A278717 * A278657 A242914 A046542

Adjacent sequences: A241006 A241007 A241008 * A241010 A241011 A241012

Keyword

nonn,cons

Author

Jean-François Alcover, Aug 07 2014

Status

approved