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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 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

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