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A098686
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Decimal expansion of Sum_{n >= 1} n/(n^n).
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7
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1, 6, 2, 8, 4, 7, 3, 7, 1, 2, 9, 0, 1, 5, 8, 4, 4, 4, 7, 0, 5, 5, 8, 8, 9, 1, 4, 3, 2, 6, 1, 8, 8, 3, 0, 3, 1, 6, 5, 0, 5, 4, 0, 3, 1, 0, 9, 5, 4, 6, 2, 1, 4, 1, 6, 4, 7, 4, 1, 3, 6, 4, 3, 0, 0, 9, 2, 3, 8, 5, 9, 7, 0, 5, 1, 8, 1, 1, 9, 8, 0, 4, 8, 6, 4, 3, 2, 6, 4, 4, 0, 3, 1, 2, 9, 6, 2, 0, 5, 3, 4, 3, 6, 5, 2
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OFFSET
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1,2
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COMMENTS
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Equals 1 + Integral_{x = 0..1} x/x^x dx. More generally, for k = 0,1,2,..., Sum_{n >= k+1} n^k/n^n = Integral_{x = 0..1} x^k/x^x dx.
Also equals the double integral Integral_{x = 0..1, y = 0..1} (1 + x*y)/ (x*y)^(x*y) dx dy. Cf. A073009. (End)
Equals Integral_{x = 0..1} (1 - x*log(x))/x^x dx. - Peter Bala, Jul 21 2022
Equals Integral_{x = 0..1} (1 + x*log(x)^2)/x^x dx.
Equals the double integral Integral_{x = 0..1, y = 0..1} (x*y*log(x*y) - 1)/( (x*y)^(x*y) * log(x*y) ) dx dy and also equals 1 - Integral_{x = 0..1, y = 0..1} x*y/( (x*y)^(x*y) * log(x*y) ) dx dy by Glasser, Theorem 1. (End)
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LINKS
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EXAMPLE
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1.62847371290158444705588914326188303165054031095462141647413643009...
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MAPLE
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evalf(add(n/(n^n), n = 0..65), 100); # Peter Bala, Nov 02 2022
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MATHEMATICA
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s = 0; Do[s = N[s + n/n^n, 128], {n, 62}]; RealDigits[s, 10, 111][[1]] (* Robert G. Wilson v, Nov 03 2004 *)
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PROG
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CROSSREFS
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KEYWORD
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AUTHOR
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Joseph Biberstine (jrbibers(AT)indiana.edu), Oct 27 2004
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EXTENSIONS
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STATUS
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approved
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