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 A229171 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. 5
 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 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 LINKS EXAMPLE 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. MAPLE # A229171, A229172, A229173. 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; PROG (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 */ CROSSREFS Cf. A229172, A229173, A229175; A229168, A229169, A229170, A010062, A229167; also A004207. Sequence in context: A146523 A102260 A023383 * A092407 A056496 A106367 Adjacent sequences:  A229168 A229169 A229170 * A229172 A229173 A229174 KEYWORD nonn,more AUTHOR N. J. A. Sloane, Sep 27 2013 EXTENSIONS a(7)-a(25) from Donovan Johnson, Oct 04 2013 STATUS approved

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Last modified October 23 22:15 EDT 2019. Contains 328373 sequences. (Running on oeis4.)