A277429 Numerators of the Fabius function F(3/2^n).
67, 73, 46657, 25219, 29407171, 10997359, 109661317247, 31733679209, 558462830097043, 132566737763827, 646476041042787542443, 130499244418507180561, 2411172049639892707896547, 424191560077453917728503, 84883189962706557116984038531, 172244289373664036915914887721
Offset: 2
Examples
A277429/A277430 = 67/72, 73/288, 46657/2073600, 25219/33177600, 29407171/2809213747200, ... (starting from n = 2)
References
- Rvachev V. L., Rvachev V. A., Non-classical methods of the approximation theory in boundary value problems, Naukova Dumka, Kiev (1979) (in Russian), pages 117-125.
Links
- Yuri Dimitrov, G. A. Edgar, Solutions of Self-differential Functional Equations
- G. A. Edgar, Examples of self differential functions
- J. Fabius, A probabilistic example of a nowhere analytic C^infty-function, Probability Theory and Related Fields, June 1966, Volume 5, Issue 2, pp 173-174.
- Wikipedia, Fabius function
Programs
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Mathematica
c[0] = 1; c[k_] := c[k] = Sum[((-1)^(k - r) c[r])/(1 + 2 k - 2 r)!, {r, 0, k - 1}]/(4^k - 1); t[n_] := Mod[2 n + Sum[(-1)^Binomial[n, k], {k, 1, n}], 3]; f[x_] := Module[{k = Numerator[x], n = Log2[Denominator[x]]}, Sum[((-1)^(q + t[p - 1]) 2^(-(n - 1) n/2) (1/2 - p + k)^(n - 2 q) c[q])/(4^q (n - 2 q)!), {p, 1, k}, {q, 0, n/2}]]; Table[Numerator[f[3/2^n]], {n, 2, 20}]
Comments