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A227689 a(n) is the least integer k such that 2^k - 1 has at least 10^n digits.

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%I A227689 #28 Jun 28 2021 12:05:41
%S A227689 1,30,329,3319,33216,332190,3321925,33219278,332192807,3321928092,
%T A227689 33219280946,332192809486,3321928094885,33219280948871,
%U A227689 332192809488733,3321928094887360,33219280948873621,332192809488736232,3321928094887362345,33219280948873623476
%N A227689 a(n) is the least integer k such that 2^k - 1 has at least 10^n digits.
%H A227689 Alois P. Heinz, <a href="/A227689/b227689.txt">Table of n, a(n) for n = 0..1000</a>
%H A227689 Wikipedia, <a href="http://en.wikipedia.org/wiki/Great_Internet_Mersenne_Prime_Search">Great Internet Mersenne Prime Search</a>
%F A227689 a(n) = ceiling(log_2(10^(10^n-1)+1)).
%F A227689 Limit_{n -> oo} a(n)/10^n = log_2(10) = A020862. - _Alois P. Heinz_, Jun 28 2021
%e A227689 For n = 2, A000225(328) has 99 digits and A000225(329) has 100 digits, so a(2) = 329.
%o A227689 (PARI) a(n) = ceil(log(10^(10^n-1)+1)/log(2)); \\ _Michel Marcus_, Jun 28 2021
%Y A227689 See A000225, A020862, A034887.
%K A227689 nonn,base
%O A227689 0,2
%A A227689 _Olivier de Mouzon_, Jul 19 2013
%E A227689 a(7)-a(19) from _Alois P. Heinz_, Jun 28 2021