A359282 Decimal expansion of Integral_{x = 0..1} 1/x^(x^2) dx.

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, 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, 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

Offset

1,4

Links

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

Wikipedia, Sophomore's Dream

Formula

Equals Sum_{n >= 1} 1/(2*n - 1)^n.

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).

Example

1.119545120136127596612676247029827036460046957876427628986749 ...

Maple

evalf(Sum(1/(2*n-1)^n, n = 1..infinity), 120);

Mathematica

NIntegrate[x^(-x^2), {x, 0, 1}, WorkingPrecision -> 103] // RealDigits // First

Prog

(PARI) intnum(x = 0, 1, x^(-x^2))

Crossrefs

Cf. A073009, A083648, A253299, A359283, A359284, A359285, A359286.

Sequence in context: A071831 A245294 A110894 * A198933 A353772 A259148

Adjacent sequences: A359279 A359280 A359281 * A359283 A359284 A359285

Keyword

nonn,cons,easy

Author

Peter Bala, Dec 24 2022

Status

approved