A229171 - OEIS

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

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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];