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Number of decimal digits in Mersenne(10^n).
0

%I #10 Feb 16 2025 08:32:59

%S 1,4,31,302,3011,30103,301030,3010300,30103000,301029996,3010299957,

%T 30102999567,301029995664,3010299956640,30102999566399,

%U 301029995663982,3010299956639812,30102999566398120

%N Number of decimal digits in Mersenne(10^n).

%C Digits approach expansion of log_10(2) = 0.30102999... (A007524).

%H Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/MersenneNumber.html">Mersenne Number</a>

%p seq(length(2^(10^n)),n=0..6); # _Zerinvary Lajos_, Apr 20 2008

%t Table[Floor[10^n Log[10, 2]]+1, {n, 0, 17}]

%Y Cf. A000225, A007524.

%K nonn,base,changed

%O 0,2

%A _Eric W. Weisstein_, Nov 30 2005