A369499 Decimal expansion of exp(sqrt(3)*Pi/18)/3^(1/4).
1, 0, 2, 8, 0, 3, 2, 5, 4, 1, 6, 8, 9, 5, 7, 6, 7, 7, 0, 4, 6, 2, 8, 8, 4, 3, 5, 7, 8, 5, 7, 7, 2, 1, 6, 7, 7, 8, 9, 2, 4, 1, 8, 6, 2, 6, 5, 4, 0, 0, 2, 2, 3, 9, 5, 4, 0, 6, 8, 8, 1, 6, 2, 8, 0, 3, 8, 0, 5, 3, 4, 7, 2, 2, 7, 0, 9, 7, 9, 0, 1, 0, 6, 6, 7, 1, 0, 7, 6, 7, 2, 0, 0, 9, 7, 0, 6, 9, 1, 7, 1, 3, 0, 5, 0, 3, 3, 4, 0, 3, 4, 5, 6, 1, 5, 0, 6, 7, 0, 8
Offset: 1
Examples
1.02803254168957677046288435785772167789241862654002...
Links
- Albert Stadler, Problem 11677, Problems and Solutions, The American Mathematical Monthly, Vol. 119, No. 10 (2012), p. 880; Dedekind eta Function Disguised, Solution to Problem 11677 by Radouan Boukharfane, ibid., Vol. 121, No. 10 (December 2014), pp. 951-952. Note that the problem appeared with typos.
- Allen Stenger, Experimental Math for Math Monthly Problems, The American Mathematical Monthly, Vol. 124, No. 2 (2017), pp. 116-131; alternative link. See pp. 129-130.
Crossrefs
Cf. A011002.
Programs
-
Mathematica
RealDigits[Exp[Sqrt[3]*Pi/18]/3^(1/4), 10, 120][[1]]
-
PARI
exp(sqrt(3)*Pi/18)/sqrtn(3, 4)
Formula
Equals Product_{k>=1} (1 + 2*exp(-k*Pi*sqrt(3)) * cosh(k*Pi/sqrt(3))) (Stadler, 2012).