|
%I #12 Dec 28 2022 02:03:28
%S 1,1,1,9,5,4,5,1,2,0,1,3,6,1,2,7,5,9,6,6,1,2,6,7,6,2,4,7,0,2,9,8,2,7,
%T 0,3,6,4,6,0,0,4,6,9,5,7,8,7,6,4,2,7,6,2,8,9,8,6,7,4,9,5,4,6,7,5,7,0,
%U 9,4,4,0,8,3,4,4,3,2,8,3,9,8,7,5,6,8,6,2,6,4,5,3,8,2,0,1,0,7,7,3,0,0,5,9,7,9,9,4
%N Decimal expansion of Integral_{x = 0..1} 1/x^(x^2) dx.
%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Sophomore%27s_dream">Sophomore's Dream</a>
%F Equals Sum_{n >= 1} 1/(2*n - 1)^n.
%F More generally, Integral_{x = 0..1} 1/x^(t*x^2) dx = Sum_{n >= 1} t^(n-1)/(2*n - 1)^n. See A253299 (case t = -1).
%e 1.119545120136127596612676247029827036460046957876427628986749 ...
%p evalf(Sum(1/(2*n-1)^n, n = 1..infinity), 120);
%t NIntegrate[x^(-x^2), {x, 0, 1}, WorkingPrecision -> 103] // RealDigits // First
%o (PARI) intnum(x = 0, 1, x^(-x^2))
%Y Cf. A073009, A083648, A253299, A359283, A359284, A359285, A359286.
%K nonn,cons,easy
%O 1,4
%A _Peter Bala_, Dec 24 2022
|
