A331122 Nearest integer to Integral_{x=0..n} x^x dx.

0, 1, 3, 15, 114, 1242, 17129, 284714, 5526741, 122592633, 3057488913, 84665033543, 2576896828787, 85495426794698, 3070641026296061, 118685141706060740, 4911825483278949553, 216697390123422589527, 10151899714746097960699, 503310218588181014061292

Offset

0,3

Comments

The antiderivative of x^x cannot be described in terms of elementary functions.

a(1)=1 is the rounding of A083648.

Links

Table of n, a(n) for n=0..19.

Eric Weisstein's World of Mathematics, Sophomore's Dream

Example

Integral_{X=0..4} x^x dx = 114.119062..., so a(4) = 114.
Integral_{x=0..7} x^x dx = 284713.7347218579997..., so a(7) = 284714.

Mathematica

Table[Round[NIntegrate[x^x, {x, 0, n}, WorkingPrecision->100]], {n, 0, 20}] (* Harvey P. Dale, Nov 04 2020 *)

Prog

(PARI) for(k=0, 19, print1(round(intnum(x=0, k, x^x)), ", ")) \\ Hugo Pfoertner, Jan 18 2020

Crossrefs

Cf. A000312, A083648.

Sequence in context: A166885 A346224 A082163 * A342167 A346272 A190629

Adjacent sequences: A331119 A331120 A331121 * A331123 A331124 A331125

Keyword

nonn

Author

Eliora Ben-Gurion, Jan 10 2020

Status

approved