|
%I #8 Dec 28 2022 02:27:34
%S 1,0,6,5,5,1,8,2,0,5,9,2,7,6,4,9,1,7,5,8,6,3,8,2,1,4,0,5,4,8,4,5,4,7,
%T 2,3,1,5,3,9,8,0,2,2,7,9,0,9,9,8,2,1,2,4,8,9,8,9,2,8,4,5,6,5,8,7,8,3,
%U 0,3,2,5,6,8,1,2,4,5,7,0,0,0,3,8,3,0,1,9,3,5,7,6,1,2,3,9,9,4,0,9,2,8,7,9,2,7,9,0
%N Decimal expansion of Integral_{x = 0..1} 1/x^(x^3) dx.
%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Sophomore%27s_dream">Sophomore's Dream</a>
%F Equals Sum_{n >= 1} 1/(3*n - 2)^n.
%F More generally, Integral_{x = 0..1} 1/x^(t*x^3) dx = Sum_{n >= 1} t^(n-1)/(3*n - 2)^n. See A359285 (case t = -1).
%e 1.06551820592764917586382140548454723153980227909982...
%p evalf(int(1/x^(x^3), x = 0..1), 110);
%t NIntegrate[1/x^(x^3), {x, 0, 1}, WorkingPrecision -> 110] // RealDigits // First
%o (PARI) intnum(x = 0, 1, x^(-x^3))
%Y Cf. A245637, A253299, A359282, A359283, A359285, A359286.
%K nonn,cons,easy
%O 1,3
%A _Peter Bala_, Dec 24 2022
|
