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 A076949 Decimal expansion of c, the constant such that lim n -> infinity A003095(n)/c^(2^n) = 1. 9
 1, 2, 2, 5, 9, 0, 2, 4, 4, 3, 5, 2, 8, 7, 4, 8, 5, 3, 8, 6, 2, 7, 9, 4, 7, 4, 9, 5, 9, 1, 3, 0, 0, 8, 5, 2, 1, 3, 2, 1, 2, 2, 9, 3, 2, 0, 9, 6, 9, 6, 6, 1, 2, 8, 2, 3, 1, 7, 7, 0, 0, 9, 0, 7, 2, 5, 5, 2, 3, 3, 9, 9, 7, 5, 2, 6, 5, 7, 3, 8, 0, 2, 1, 6, 7, 9, 1, 5, 4, 5, 2, 0, 4, 9, 9, 2, 8, 4, 2, 9 (list; constant; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 LINKS G. C. Greubel, Table of n, a(n) for n = 1..10000 Stephan Wagner, Volker Ziegler, Irrationality of growth constants associated with polynomial recursions, arXiv:2004.09353 [math.NT], 2020. FORMULA Equals sqrt(A077496). - Vaclav Kotesovec, Dec 17 2014 EXAMPLE 1.2259024435287485386279474959130085213212293209696612823177009072552339975... MATHEMATICA A003095[n_]:= A003095[n]= If[n==0, 0, 1 + A003095[n-1]^2]; S[n_]:= S[n]= If[n==1, Log[2]/2, S[n-1] + Log[1 + 1/A003095[n]^2]/2^n]; RealDigits[Exp[S[13]/2], 10, 120][[1]] (* G. C. Greubel, Nov 29 2022 *) PROG (Magma) function A003095(n) if n eq 0 then return 0; else return 1 + A003095(n-1)^2; end if; return A003095; end function; function S(n) if n eq 1 then return Log(2)/2; else return S(n-1) + Log(1 + 1/A003095(n)^2)/2^n; end if; return S; end function; SetDefaultRealField(RealField(120)); Exp(S(12)/2); // G. C. Greubel, Nov 29 2022 (SageMath) @CachedFunction def A003095(n): return 0 if (n==0) else 1 + A003095(n-1)^2 @CachedFunction def S(n): return log(2)/2 if (n==1) else S(n-1) + log(1 + 1/(A003095(n))^2)/2^n numerical_approx( exp(S(12)/2), digits=120) # G. C. Greubel, Nov 29 2022 CROSSREFS Cf. A003095, A077496, A213437, A258112, A258113. Sequence in context: A344036 A208938 A019086 * A040009 A227527 A275504 Adjacent sequences: A076946 A076947 A076948 * A076950 A076951 A076952 KEYWORD cons,nonn AUTHOR Benoit Cloitre, Nov 27 2002 STATUS approved

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Last modified September 19 14:36 EDT 2024. Contains 376012 sequences. (Running on oeis4.)