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A226574
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Decimal expansion of lim_{k->oo} f(k), where f(1)=e, and f(k) = e + log(f(k-1)) for k>1.
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5
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4, 1, 3, 8, 6, 5, 1, 9, 4, 6, 4, 7, 9, 1, 2, 8, 6, 9, 3, 8, 1, 8, 7, 0, 8, 7, 5, 5, 2, 5, 2, 4, 3, 5, 4, 7, 8, 3, 4, 3, 6, 7, 4, 4, 3, 0, 4, 6, 4, 8, 5, 4, 8, 1, 1, 2, 9, 4, 4, 3, 1, 6, 3, 9, 3, 5, 4, 0, 5, 1, 8, 4, 4, 3, 6, 7, 5, 5, 3, 9, 3, 0, 4, 2, 7, 1
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OFFSET
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1,1
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COMMENTS
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Let g(x) be the greater of the two solutions of s + log(s) = x; then A226572 represents g(e). [See however the comments in A226571. - N. J. A. Sloane, Dec 09 2017]
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LINKS
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FORMULA
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EXAMPLE
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limit(f(n)) = 4.1386519474...
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MATHEMATICA
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f[s_, accuracy_] := FixedPoint[N[s - Log[#], accuracy] &, 1]
g[s_, accuracy_] := FixedPoint[N[s + Log[#], accuracy] &, 1]
d1 = RealDigits[f[E, 200]][[1]] (* A226573 *)
d2 = RealDigits[g[E, 200]][[1]] (* A226574 *)
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PROG
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(PARI) default(realprecision, 100); solve(x=4, 5, x - log(x) - exp(1)) \\ Jianing Song, Dec 24 2018
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CROSSREFS
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KEYWORD
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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