A379605 Decimal expansion of sigma_sup = sup{real(s): Psi(s) = 0}, where Psi(s) = Sum_{n>=1} 1/n!^s.
7, 2, 6, 3, 4, 7, 5, 0, 8, 5, 7, 6, 2, 0, 1, 1, 4, 5, 9, 4, 1, 6, 4, 0, 2, 6, 2, 2, 6, 9, 5, 2, 3, 2, 5, 0, 8, 5, 0, 1, 3, 4, 3, 3, 4, 3, 0, 0, 6, 4, 1, 2, 7, 8, 1, 8, 4, 6, 8, 3, 6, 3, 4, 1, 2, 6, 5, 6, 2, 9, 9, 1, 7, 8, 3, 2, 3, 2, 9, 9, 1, 1, 9, 3, 4, 0, 8, 9, 2, 3, 5, 9, 0, 6, 4, 4, 6, 9, 8, 3
Offset: 0
Examples
0.726347508576201145941640262269523250850134334300641278184683634...
Links
- MathOverflow.net, The location of the zeros of the "new" function Psi.
- Roberto Trocchi, The Psi function and its zeros on the complex plane - Version 2.0, December 27 2024.
Crossrefs
Cf. A373204.
Programs
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Mathematica
Nmax = 200; Cn = {1}; kn = {0}; For[n = 2, n <= Nmax, n = n + 1, If[PrimeQ[n], If[Cn[[n - 1]] == 1, AppendTo[kn, 1], AppendTo[kn, 0]]; AppendTo[Cn, -1], PF = FactorInteger[n]; For[m = 1; somma = 0, m <= Length[PF], m = m + 1, somma = somma + kn[[PF[[m]][[1]]]]*PF[[m]][[2]]]; AppendTo[kn, Mod[somma, 2]]; If[kn[[n]] == 0, AppendTo[Cn, Cn[[n - 1]]], AppendTo[Cn, -Cn[[n - 1]]]]]] NSolveValues[ {Sum[Cn[[n]]*n!^-sigma, {n, 1, Nmax}] == 0, sigma > 1/10, sigma < 1}, sigma, WorkingPrecision -> 200][[1]]
Formula
sigma_sup = sup{real(s): Psi(s) = 0}, where Psi(s) = Sum_{n>=1} 1/n!^s.
Comments