cp's OEIS Frontend

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.

%I A229171 #18 Nov 05 2013 20:13:37
%S A229171 1,5,10,20,41,86,192,441,1039,2493,6072,14960,37199,93193,234957,
%T A229171 595562,1516639,3877905,9950908,25615654,66127187,171144672,443966371,
%U A229171 1154115393,3005950908
%N 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.
%H A229171 <a href="/index/Coi#Colombian">Index entries for Colombian or self numbers and related sequences</a>
%e A229171 The initial terms of the b(n) sequence are approximately
%e A229171 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, ...
%e A229171 b(5) is the first term >= e^2, so a(2) = 5.
%p A229171 # A229171, A229172, A229173.
%p A229171 Digits:=24;
%p A229171 e:=evalf(exp(1));
%p A229171 lis:=[e]; a:=e;
%p A229171 t1:=[1]; l:=2;
%p A229171 for i from 2 to 128 do
%p A229171 a:=evalf(a+log(a));
%p A229171 if a >= e^l then
%p A229171 l:=l+1; t1:=[op(t1),i]; fi;
%p A229171 lis:=[op(lis),a];
%p A229171 od:
%p A229171 lis;
%p A229171 map(floor,lis);
%p A229171 map(ceil,lis);
%p A229171 t1;
%o A229171 (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 */
%Y A229171 Cf. A229172, A229173, A229175; A229168, A229169, A229170, A010062, A229167; also A004207.
%K A229171 nonn,more
%O A229171 1,2
%A A229171 _N. J. A. Sloane_, Sep 27 2013
%E A229171 a(7)-a(25) from _Donovan Johnson_, Oct 04 2013