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A291840
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Decimal expansion of the constant c in the asymptotic formula for A291839.
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2
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2, 2, 6, 2, 8, 7, 5, 8, 3, 2, 5, 6, 2, 6, 2, 1, 2, 4, 6, 3, 0, 2, 3, 3, 3, 3, 5, 8, 3, 8, 4, 3, 6, 5, 9, 3, 8, 9, 0, 6, 8, 0, 4, 1, 9, 6, 3, 9, 5, 3, 7, 1, 0, 5, 2, 7, 1, 2, 7, 1, 6, 3, 3, 4, 1, 8, 5, 4, 7, 3, 8, 9, 7, 1, 2, 9, 9, 4, 8
(list;
constant;
graph;
refs;
listen;
history;
text;
internal format)
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OFFSET
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1,1
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LINKS
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FORMULA
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Equals mu(A266389), where function t->mu(t) is defined in the PARI code.
Constant c where A291839(n) ~ c*n + o(sqrt(n)).
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EXAMPLE
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2.262875832562621246302333358384...
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PROG
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(PARI)
x(t) = (1+3*t)*(1/t-1)^3/16;
y(t) = {
my(y1 = t^2 * (1-t) * (18 + 36*t + 5*t^2),
y2 = 2 * (3+t) * (1+2*t) * (1+3*t)^2);
(1+2*t)/((1+3*t) * (1-t)) * exp(-y1/y2) - 1;
};
alpha(t) = 144 + 592*t + 664*t^2 + 135*t^3 + 6*t^4 - 5*t^5;
mu(t) = {
my(mu1 = (1+t) * (3+t)^2 * (1+2*t)^2 * (1+3*t)^2 / t^3, y0 = y(t));
mu1 * y0 / ((1 + y0) * alpha(t));
};
N=79; default(realprecision, N+100); t0 = solve(t=.62, .63, y(t)-1);
c=mu(t0); eval(select(x->(x != "."), Vec(Str(c))[1..-101]))
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CROSSREFS
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KEYWORD
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AUTHOR
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STATUS
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approved
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