

A083648


Decimal expansion of Sum_{n=1..Infinity} (1)^n/n^n = Integral_{x=0..1} x^x dx.


9



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

0,1


COMMENTS

In 1697, Johann Bernoulli explores this curve and finds its minimum and the area under the curve from 0 to 1, all this without the benefit of the exponential function.


REFERENCES

William Dunham, The Calculus Gallery, Masterpieces from Newton to Lebesgue, Princeton University Press, Princeton, NJ 2005, page 4651.
Paul J. Nahin, An Imaginary Tale: The Story of sqrt(1), Princeton, New Jersey: Princeton University Press (1988) page 146.


LINKS

Table of n, a(n) for n=0..104.
Eric Weisstein's World of Mathematics, Power Tower
Eric Weisstein's World of Mathematics, Sophomore's Dream


FORMULA

Constant also equals the double integral int {y = 0..1} int {x = 0..1} (x*y)^(x*y) dx dy.  Peter Bala, Mar 04 2012


EXAMPLE

0.78343051071213440705926438652697546940768199014693095825541782270...


MATHEMATICA

RealDigits[ Sum[ (1)^n /n^n, {n, 1, 60}], 10, 111] [[1]] (* Robert G. Wilson v, Jan 31 2005 *)


PROG

(PARI) sumalt(n=1, (1/n)^(n)) \\ Michel Marcus, Oct 15 2015


CROSSREFS

Cf. A073009. The minimum point on the curve x^x is (A068985, A072364).
Sequence in context: A064207 A020843 A241296 * A133613 A194622 A193010
Adjacent sequences: A083645 A083646 A083647 * A083649 A083650 A083651


KEYWORD

cons,nonn


AUTHOR

Eric W. Weisstein, May 01 2003


STATUS

approved



