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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
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 (list; constant; graph; refs; listen; history; text; internal format)
OFFSET
1,2
REFERENCES
Steven R. Finch, Mathematical Constants, Cambridge University Press, 2003, Section 2.10 Sierpinski's constant, p. 122.
LINKS
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
Sequence in context: A357102 A258149 A278717 * A278657 A242914 A046542
KEYWORD
nonn,cons
AUTHOR
STATUS
approved

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Last modified March 4 22:06 EST 2024. Contains 370532 sequences. (Running on oeis4.)