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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

Table of n, a(n) for n=1..105.

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-Fran├žois Alcover, Jun 18 2014 *)

CROSSREFS

Cf. A001699, A003095, A076949.

Sequence in context: A195720 A198883 A261850 * A190913 A019106 A051566

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 February 24 21:22 EST 2018. Contains 299628 sequences. (Running on oeis4.)