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 A077496 Decimal expansion of lim n -> infinity A001699(n)^(1/2^n). 3
 1, 5, 0, 2, 8, 3, 6, 8, 0, 1, 0, 4, 9, 7, 5, 6, 4, 9, 9, 7, 5, 2, 9, 3, 6, 4, 2, 3, 7, 3, 2, 1, 6, 9, 4, 0, 8, 7, 3, 8, 8, 7, 1, 7, 4, 3, 9, 6, 3, 5, 7, 9, 3, 0, 6, 9, 9, 0, 6, 7, 1, 4, 2, 4, 3, 0, 8, 4, 7, 1, 9, 7, 8, 7, 1, 7, 5, 7, 6, 6, 0, 1, 9, 4, 5, 6, 6, 3, 3, 3, 9, 1, 7, 8, 6, 3, 0, 6, 1, 9, 8, 7, 2, 3, 7 (list; constant; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 REFERENCES Steven R. Finch, Mathematical Constants, Cambridge University Press, 2003, Section 6.10 Quadratic recurrence constants, p. 443. LINKS A. De Mier, M. Noy, On the maximum number of cycles in outerplanar and series-parallel graphs, El. Notes Discr. Math. 34 (2009) 489-493, Proposition 2.2. Eric Weisstein's World of Mathematics, Quadratic Recurrence Equation FORMULA lim n -> infinity A001699(n)^(1/2^n) = 1.50283680104975649975293642... Equals A076949^2. - Vaclav Kotesovec, Dec 17 2014 EXAMPLE 1.5028368010497564997529364237321694087388717439635793069906714243... MATHEMATICA digits = 105; Clear[b, beta]; b[0] = 1; b[n_] := b[n] = b[n-1]^2 + 1; b[10]; beta[n_] := beta[n] = b[n]^(2^(-n)); beta[5]; beta[n = 6]; While[ RealDigits[beta[n], 10, digits+5] != RealDigits[beta[n-1], 10, digits+5], Print["n = ", n]; n = n+1]; RealDigits[beta[n], 10, digits] // First (* Jean-François Alcover, Jun 18 2014 *) CROSSREFS Cf. A001699, A003095, A076949. Sequence in context: A195720 A198883 A261850 * A346120 A190913 A019106 Adjacent sequences:  A077493 A077494 A077495 * A077497 A077498 A077499 KEYWORD cons,nonn AUTHOR Benoit Cloitre, Dec 01 2002 STATUS approved

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Last modified January 16 18:07 EST 2022. Contains 350376 sequences. (Running on oeis4.)