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 A092526 Decimal expansion of (2/3)*cos( (1/3)*arccos(29/2) ) + 1/3, the real root of x^3 - x^2 - 1. 15
 1, 4, 6, 5, 5, 7, 1, 2, 3, 1, 8, 7, 6, 7, 6, 8, 0, 2, 6, 6, 5, 6, 7, 3, 1, 2, 2, 5, 2, 1, 9, 9, 3, 9, 1, 0, 8, 0, 2, 5, 5, 7, 7, 5, 6, 8, 4, 7, 2, 2, 8, 5, 7, 0, 1, 6, 4, 3, 1, 8, 3, 1, 1, 1, 2, 4, 9, 2, 6, 2, 9, 9, 6, 6, 8, 5, 0, 1, 7, 8, 4, 0, 4, 7, 8, 1, 2, 5, 8, 0, 1, 1, 9, 4, 9, 0, 9, 2, 7, 0, 0, 6, 4, 3, 8 (list; constant; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS This is the limit x of the ratio N(n+1)/N(n) for n -> infinity of the Narayana sequence N(n) = A000930(n). The real root of x^3 - x^2 - 1. See the formula section. - Wolfdieter Lang, Apr 24 2015 This is the fourth smallest Pisot number. - Iain Fox, Oct 13 2017 Sometimes called the supergolden ratio or Narayana's cows constant, and denoted by the symbol psi. - Ed Pegg Jr, Feb 01 2019 REFERENCES S. R. Finch, Mathematical Constants, Cambridge, 2003, Section 1.2.3. Paul J. Nahin, The Logician and the Engineer, How George Boole and Claude Shannon Created the Information Age, Princeton University Press, Princeton and Oxford, 2013, Chap. 7: Some Combinational Logic Examples, Section 7.1: Channel Capacity, Shannon's Theorem, and Error-Detection Theory, page 120. LINKS Harry J. Smith, Table of n, a(n) for n = 1..20000 Simon Baker, Exceptional digit frequencies and expansions in non-integer bases, arXiv:1711.10397 [math.DS], 2017. See the beta(2) constant pp. 3-4. H. R. P. Ferguson, On a Generalization of the Fibonacci Numbers Useful in Memory Allocation Schema or All About the Zeroes of Z^k - Z^{k - 1} - 1, k > 0, Fibonacci Quarterly, Volume 14, Number 3, October, 1976 (see Table 2, p. 238). Ed Pegg Jr., Images based on the supergolden ratio Wikipedia, Pisot number Wikipedia, Supergolden ratio FORMULA The real root of x^3 - x^2 - 1. - Franklin T. Adams-Watters, Oct 12 2006 The only real irrational root of x^4-x^2-x-1 (-1 is also a root). [Nahim] (2/3)*cos( (1/3)*arccos(29/2) ) + 1/3. Equals 1 + A088559. Equals (1/6)*(116+12*sqrt(93))^(1/3) + 2/(3*(116+12*sqrt(93))^(1/3)) + 1/3. - Vaclav Kotesovec, Dec 18 2014 Equals 1/A263719. - Alois P. Heinz, Apr 15 2018 EXAMPLE 1.46557123187676802665673122521993910802557756847228570164318311124926... MATHEMATICA RealDigits[(2 Cos[ ArcCos[ 29/2]/3] + 1)/3, 10, 111][[1]] (* Robert G. Wilson v, Apr 12 2004 *) RealDigits[ Solve[ x^3 - x^2 - 1 == 0, x][[1, 1, 2]], 10, 111][[1]] (* Robert G. Wilson v, Oct 10 2013 *) PROG (PARI) { allocatemem(932245000); default(realprecision, 20080); x=solve(x=1, 2, x^3 - x^2 - 1); for (n=1, 20000, d=floor(x); x=(x-d)*10; write("b092526.txt", n, " ", d)); } \\ Harry J. Smith, Jun 21 2009 CROSSREFS Cf. A088559, A076725, A000930, A263719. Other Pisot numbers: A060006, A086106, A228777, A293506, A293508, A293509, A293557. Sequence in context: A200497 A271365 A088559 * A243396 A140243 A199289 Adjacent sequences:  A092523 A092524 A092525 * A092527 A092528 A092529 KEYWORD nonn,cons,easy AUTHOR N. J. A. Sloane, Apr 07 2004 STATUS approved

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Last modified February 23 04:44 EST 2019. Contains 320411 sequences. (Running on oeis4.)