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A226574
Decimal expansion of lim_{k->oo} f(k), where f(1)=e, and f(k) = e + log(f(k-1)) for k>1.
5
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
OFFSET
1,1
COMMENTS
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]
LINKS
FORMULA
Equals -LambertW(-1, -exp(-e)). - Jianing Song, Dec 24 2018
EXAMPLE
limit(f(n)) = 4.1386519474...
MATHEMATICA
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 *)
PROG
(PARI) default(realprecision, 100); solve(x=4, 5, x - log(x) - exp(1)) \\ Jianing Song, Dec 24 2018
CROSSREFS
KEYWORD
nonn,cons,easy
AUTHOR
Clark Kimberling, Jun 12 2013
EXTENSIONS
Definition revised by N. J. A. Sloane, Dec 09 2017
STATUS
approved