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A245330 Decimal expansion of phi(0), an auxiliary constant associated with Shapiro's cyclic sum constant lambda. 2
9, 8, 9, 1, 3, 3, 6, 3, 4, 4, 4, 6, 9, 9, 3, 0, 5, 2, 2, 4, 3, 4, 9, 0, 3, 0, 8, 2, 6, 6, 3, 3, 7, 9, 8, 1, 3, 8, 0, 3, 4, 8, 0, 9, 8, 0, 4, 4, 1, 8, 2, 2, 1, 9, 0, 3, 9, 3, 5, 7, 8, 7, 8, 0, 8, 7, 3, 8, 2, 8, 9, 5, 4, 2, 6, 7, 5, 7, 9, 5, 8, 1, 5, 3, 8, 0, 3, 7, 6, 7, 5, 0, 8, 8, 0, 8, 0, 3, 8, 9, 4, 2, 4 (list; constant; graph; refs; listen; history; text; internal format)
OFFSET

0,1

REFERENCES

Steven R. Finch, Mathematical Constants, Cambridge University Press, 2003, Section 3.1 Shapiro-Drinfeld Constant, p. 209.

LINKS

Table of n, a(n) for n=0..102.

Eric Weisstein's MathWorld, Shapiro's Cyclic Sum Constant

FORMULA

lambda = A086277 = phi(0)/2.

EXAMPLE

0.989133634446993052243490308266337981380348098044182219039357878...

MATHEMATICA

digits = 103; phi[0] = (2 + x + 2*E^(x/2)*(1+x))/(E^(x/2)*(1+E^(x/2))^2) /. FindRoot[E^(x/2)*(1+E^(x/2))^2/(1+2*E^(x/2)) == E^(1/(1+2*E^(x/2)) + x), {x, 0}, WorkingPrecision -> digits+10]; RealDigits[phi[0], 10, digits] // First

CROSSREFS

Cf. A086277.

Sequence in context: A090998 A163930 A157371 * A269222 A201994 A243277

Adjacent sequences:  A245327 A245328 A245329 * A245331 A245332 A245333

KEYWORD

nonn,cons

AUTHOR

Jean-Fran├žois Alcover, Jul 18 2014

STATUS

approved

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Last modified November 20 13:03 EST 2019. Contains 329336 sequences. (Running on oeis4.)