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A073009 Decimal expansion of Sum_{n >= 1} 1/n^n. 28
1, 2, 9, 1, 2, 8, 5, 9, 9, 7, 0, 6, 2, 6, 6, 3, 5, 4, 0, 4, 0, 7, 2, 8, 2, 5, 9, 0, 5, 9, 5, 6, 0, 0, 5, 4, 1, 4, 9, 8, 6, 1, 9, 3, 6, 8, 2, 7, 4, 5, 2, 2, 3, 1, 7, 3, 1, 0, 0, 0, 2, 4, 4, 5, 1, 3, 6, 9, 4, 4, 5, 3, 8, 7, 6, 5, 2, 3, 4, 4, 5, 5, 5, 5, 8, 8, 1, 7, 0, 4, 1, 1, 2, 9, 4, 2, 9, 7, 0, 8, 9, 8, 4, 9, 9 (list; constant; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

This is also equal to Integral_{x = 0 .. 1 } 1/x^x.

10*Sum_{n = 1 .. infinity} 1/p(n)^p(n+1), where p(n) and p(n+1) are consecutive primes, is equal to Sum_{n = 1 .. infinity} 1/n^n up to the fifth decimal digit. - Paolo P. Lava, May 21 2013

LINKS

Kenny Lau, Table of n, a(n) for n = 1..10001

Johan Bernoulli, Demonstratio Methodi Analyticae, qua usus est pro determinanda aliqua Quadratura exponentiali per seriem, Actis Eruditorum A (1697), p. 131. Collected in Opera Omnia, vol. 3, 1742. See p. 376ff.

Randall Munroe, Approximations

Simon Plouffe, Sum(1/n^n,n=1..infinity)

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} 1/(x*y)^(x*y) dx dy. - Peter Bala, Mar 04 2012

Approximately log(3)^e, see Munroe link. - Charles R Greathouse IV, Apr 25 2012

Another approximation is A + A^(-19), where A is Glaisher-Kinkelin constant (A074962). - Noam Shalev, Jan 16 2015

EXAMPLE

1.291285997062663540407282590595600541498619368...

MAPLE

evalf(Sum(1/n^n, n=1..infinity), 120); # Vaclav Kotesovec, Jun 24 2016

MATHEMATICA

RealDigits[N[Sum[1/n^n, {n, 1, Infinity}], 110]] [[1]]

PROG

(PARI) suminf(n=1, n^-n) \\ Charles R Greathouse IV, Apr 25 2012

CROSSREFS

Cf. A083648, A229191, A245637.

Sequence in context: A094242 A199381 A083649 * A011064 A086773 A176124

Adjacent sequences:  A073006 A073007 A073008 * A073010 A073011 A073012

KEYWORD

cons,nonn

AUTHOR

Robert G. Wilson v, Aug 03 2002

STATUS

approved

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Last modified December 6 15:01 EST 2016. Contains 278781 sequences.