A123852 Decimal expansion of (1*(2*(3*...)^(1/3))^(1/3))^(1/3).
1, 1, 5, 6, 3, 6, 2, 6, 8, 4, 3, 3, 2, 2, 6, 9, 7, 1, 6, 8, 5, 3, 3, 7, 0, 3, 2, 2, 8, 8, 7, 3, 6, 9, 3, 5, 6, 5, 1, 3, 0, 1, 4, 5, 4, 3, 8, 9, 1, 8, 8, 8, 6, 3, 7, 9, 9, 9, 2, 5, 9, 5, 9, 8, 9, 8, 3, 1, 7, 7, 8, 1, 6, 0, 7, 2, 8, 2, 6, 1, 9, 4, 6, 0, 7, 9, 0, 8, 1, 3, 3, 8, 2, 0, 3, 7, 8, 3, 1, 7
Offset: 1
Examples
1.156362684332269716853370322887369356513014543891888637999259598983177816...
References
- Steven R. Finch, Mathematical Constants, Cambridge University Press, Cambridge, 2003, p. 446.
Links
- Kh. Hessami Pilehrood and T. Hessami Pilehrood, Vacca-type series for values of the generalized-Euler-constant function and its derivative, arXiv:0808.0410 [math.NT], 2008.
- Kh. Hessami Pilehrood and T. Hessami Pilehrood, Vacca-type series for values of the generalized-Euler-constant function and its derivative, Journal of Integer Sequences 13 (2010), Article 10.7.3.
- Jonathan Sondow and Petros Hadjicostas, The generalized-Euler-constant function gamma(z) and a generalization of Somos's quadratic recurrence constant, arXiv:math/0610499 [math.CA], 2006.
- Jonathan Sondow and Petros Hadjicostas, The generalized-Euler-constant function gamma(z) and a generalization of Somos's quadratic recurrence constant, J. Math. Anal. Appl. 332(1) (2007), 292-314.
- Eric Weisstein's World of Mathematics, Somos's Quadratic Recurrence Constant.
Programs
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Mathematica
Take[RealDigits[Product[N[n^3^-n,200], {n,400}]][[1]], 100] RealDigits[Exp[-D[PolyLog[n, 1/3], n]/.n->0], 10, 100][[1]] (* Jean-François Alcover, Jan 28 2014 *) -
PARI
prodinf(n=1, n^(1/3^n)) \\ Michel Marcus, Aug 03 2019
Formula
Equals Product_{n>=1} n^(1/3^n).
Extensions
References updated by R. J. Mathar, Aug 12 2010
Comments