A359286 - OEIS

%I #11 Dec 27 2022 16:53:59

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

%T 1,1,6,8,2,0,3,6,2,0,5,7,2,1,3,0,1,1,2,7,7,0,4,0,0,8,7,6,4,8,8,1,4,0,

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

%N Decimal expansion of Integral_{x = 1..oo} 1/x^(x^3) dx.

%C For a, b nonnegative integers, the alternating divergent series Sum_{n >= 0} (-1)^n*(a*n + b)^n is Borel summable to Integral_{x = 1..oo} x^(a-b-1)/x^(x^a) dx.

%H Peter Bala, <a href="/A245637/a245637.pdf">Borel summation of a family of divergent series</a>

%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Sophomore%27s_dream">Sophomore's Dream</a>

%F Equals Integral_{x = 1..oo} 1/(3*x - 2)^x dx.

%F Equals the Borel sum of the alternating divergent series Sum_{n >= 0} (-1)^n*(3*n + 2)^n. Compare with the alternating convergent series Sum_{n >= 1} (-1)^(n+1)/(3*n - 2)^n = Integral_{x = 0..1} x^(x^3) dx. See A359285.

%e 0.35854271600033996570705760779181131168203620572130...

%p evalf(int(1/x^(x^3), x = 1..infinity), 110);

%t NIntegrate[1/x^(x^3), {x, 1, Infinity}, WorkingPrecision -> 110] // RealDigits // First

%Y Cf. A245637, A253299, A359282, A359283, A359284, A359285.

%K nonn,cons,easy

%O 1,1

%A _Peter Bala_, Dec 24 2022