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

Author

Eliora Ben-Gurion, Jan 10 2020

Keywords

• nonn

Comments

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

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

Examples

			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.
		

Links

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

Crossrefs

Cf. A000312, A083648.

Programs

Mathematica

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

PARI

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