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A229171
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Define a sequence of real numbers by b(1)=e, b(n+1) = b(n) + log(b(n)); a(n) = smallest i such that b(i) >= e^n.
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5
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1, 5, 10, 20, 41, 86, 192, 441, 1039, 2493, 6072, 14960, 37199, 93193, 234957, 595562, 1516639, 3877905, 9950908, 25615654, 66127187, 171144672, 443966371, 1154115393, 3005950908
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OFFSET
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1,2
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LINKS
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EXAMPLE
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The initial terms of the b(n) sequence are approximately
2.71828182845904523536029, 3.71828182845904523536029, 5.03154351597726806940929, 6.64727031503970856301384, 8.54147660649653209023621, 10.6864105040926911986276, 13.0553833920216929230460, 15.6245839611886549261305, 18.3734295299727029212384, 21.2843351036624388705641, 24.3423064646657059114213, 27.5345223079930416816192, 30.8499628820185220765989, ...
b(5) is the first term >= e^2, so a(2) = 5.
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MAPLE
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Digits:=24;
e:=evalf(exp(1));
lis:=[e]; a:=e;
t1:=[1]; l:=2;
for i from 2 to 128 do
a:=evalf(a+log(a));
if a >= e^l then
l:=l+1; t1:=[op(t1), i]; fi;
lis:=[op(lis), a];
od:
lis;
map(floor, lis);
map(ceil, lis);
t1;
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PROG
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(PARI) n=1; m=exp(1); mn=m^n; for(i=1, 3005950908, if(m>=mn, print(n " " i); n++; mn=exp(1)^n); m=m+log(m)) /* Donovan Johnson, Oct 04 2013 */
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CROSSREFS
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KEYWORD
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nonn,more
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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