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.

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

Offset

1,2

Links

Table of n, a(n) for n=1..25.

Index entries for Colombian or self numbers and related sequences

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