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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
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
Sequence in context: A344036 A208938 A019086 * A040009 A227527 A275504
KEYWORD
cons,nonn
AUTHOR
Benoit Cloitre, Nov 27 2002
STATUS
approved

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Last modified March 29 22:15 EDT 2024. Contains 371282 sequences. (Running on oeis4.)