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A073009
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Decimal expansion of Sum_{n = 1 .. infinity} 1/n^n.
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20
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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
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OFFSET
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1,2
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COMMENTS
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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]
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LINKS
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Table of n, a(n) for n=1..105.
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
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FORMULA
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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
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EXAMPLE
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1.291285997062663540407282590595600541498619368...
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MATHEMATICA
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RealDigits[N[Sum[1/n^n, {n, 1, Infinity}], 110]] [[1]]
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PROG
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(PARI) suminf(n=1, n^-n) \\ Charles R Greathouse IV, Apr 25 2012
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CROSSREFS
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Cf. A083648.
Sequence in context: A094242 A199381 A083649 * A011064 A086773 A176124
Adjacent sequences: A073006 A073007 A073008 * A073010 A073011 A073012
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KEYWORD
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cons,nonn,changed
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AUTHOR
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Robert G. Wilson v, Aug 03 2002
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STATUS
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approved
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