A359286 Decimal expansion of Integral_{x = 1..oo} 1/x^(x^3) dx.

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, 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, 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

Offset

1,1

Comments

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.

Links

Table of n, a(n) for n=1..108.

Peter Bala, Borel summation of a family of divergent series

Wikipedia, Sophomore's Dream

Formula

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

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.

Example

0.35854271600033996570705760779181131168203620572130...

Maple

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

Mathematica

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

Crossrefs

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

Sequence in context: A021283 A212224 A020864 * A152304 A021902 A136188

Adjacent sequences: A359283 A359284 A359285 * A359287 A359288 A359289

Keyword

nonn,cons,easy

Author

Peter Bala, Dec 24 2022

Status

approved