A389107 Decimal expansion of the area under the infinite tetration curve.

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

Offset

1,2

Comments

For real values, infinite tetration converges within 1/(e^e) to e^(1/e).

Links

Table of n, a(n) for n=1..88.

Formula

Equals Integral_{x=1/(e^e)..e^(1/e)} x^x^x^... dx.

Equals -Integral_{x=1/(e^e)..e^(1/e)} W(-log(x))/log(x) dx.

Equals e^(1+1/e) - 1/e^(1+e) - Integral_{x=1/e..e} x^(1/x) dx.

Example

1.244131300651437208367262...

Mathematica

N[Exp[1+1/E]-Exp[-1-E]-Integrate[x^(1/x), {x, 1/E, E}], 20]

Crossrefs

Cf. A073229, A073230.

Sequence in context: A140734 A295633 A159778 * A243278 A378978 A307059

Adjacent sequences: A389104 A389105 A389106 * A389108 A389109 A389110

Keyword

nonn,cons

Author

Jwalin Bhatt, Sep 23 2025

Status

approved