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A331122
Nearest integer to Integral_{x=0..n} x^x dx.
0
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
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
Sequence in context: A346224 A082163 A375449 * A342167 A346272 A190629
KEYWORD
nonn
AUTHOR
Eliora Ben-Gurion, Jan 10 2020
STATUS
approved