A114857 Decimal expansion of 0th Gram point.

1, 7, 8, 4, 5, 5, 9, 9, 5, 4, 0, 4, 1, 0, 8, 6, 0, 8, 1, 6, 8, 2, 6, 3, 3, 8, 4, 1, 2, 5, 1, 9, 0, 9, 7, 0, 3, 5, 6, 9, 3, 2, 8, 7, 4, 3, 3, 6, 9, 6, 4, 5, 2, 3, 9, 2, 1, 1, 8, 1, 1, 4, 8, 5, 9, 4, 8, 1, 6, 8, 7, 0, 0, 9, 2, 0, 1, 6, 0, 9, 5, 2, 1, 1, 7, 5, 1, 3, 4, 0, 4, 0, 8, 4, 8, 8, 2, 0, 8, 6, 7, 6

Offset

2,2

Links

Table of n, a(n) for n=2..103.

Eric Weisstein's World of Mathematics, Gram Point

Example

17.8455995...

Mathematica

First[ RealDigits[t /. FindRoot[ RiemannSiegelTheta[t] == 0, {t, 17}, WorkingPrecision -> 120], 10, 102]] (* Jean-François Alcover, Jun 07 2012 *)

Prog

(PARI) g0(n)=2*Pi*exp(1+lambertw((8*n+1)/exp(1)/8)) \\ approximate location of gram(n)
th(t)=arg(gamma(1/4+I*t/2))-log(Pi)*t/2 \\ theta, but off by some integer multiple of 2*Pi
thapprox(t)=log(t/2/Pi)*t/2-t/2-Pi/8+1/48/t-1/5760/t^3
RStheta(t)=my(T=th(t)); (thapprox(t)-T)\/(2*Pi)*2*Pi+T
gram(n)=my(G=g0(n), k=n*Pi); solve(x=G-.003, G+1e-8, RStheta(x)-k)
gram(0) \\ Charles R Greathouse IV, Jan 22 2022
(PARI) solve(t=17.8, 18, 4*Pi+arg(gamma(1/4+I*t/2))-log(Pi)*t/2) \\ Charles R Greathouse IV, Mar 27 2023

Crossrefs

Cf. A114856, A114858.

Sequence in context: A197823 A011243 A194642 * A292823 A256920 A307065

Adjacent sequences: A114854 A114855 A114856 * A114858 A114859 A114860

Keyword

nonn,cons

Author

Eric W. Weisstein, Jan 02 2006

Status

approved