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A175824 Maximum unsigned integer that can be stored in n bytes.

%I A175824 #16 Aug 14 2024 10:14:56
%S A175824 0,255,65535,16777215,4294967295,1099511627775,281474976710655,
%T A175824 72057594037927935,18446744073709551615,4722366482869645213695,
%U A175824 1208925819614629174706175,309485009821345068724781055
%N A175824 Maximum unsigned integer that can be stored in n bytes.
%C A175824 All a(n) for n > 0 are Mersenne numbers. None are Mersenne primes.
%H A175824 Wikipedia, <a href="http://en.wikipedia.org/wiki/Byte">Byte</a>
%H A175824 Wikipedia, <a href="http://en.wikipedia.org/wiki/Mersenne_prime">Mersenne prime</a>
%H A175824 <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (257, -256).
%F A175824 a(n) = 2^(8*n) - 1.
%F A175824 a(n) = (A001025(n) - 1) * (A024036(n)^2 + A004171(n)); this relation is (x^(8*n)-1) = (x^(4*n)-1)*((x^(2*n)-1)^2 + 2*x^(2*n)) for x=2. [_Reinhard Zumkeller_, Jun 23 2011]
%e A175824 a(0) = 2^0 - 1 = 1 - 1 = 0
%e A175824 a(1) = 2^8 - 1 = 256 - 1 = 255
%e A175824 a(2) = 2^16 - 1 = 65536 - 1 = 65535
%e A175824 a(3) = 2^24 - 1 = 16777216 - 1 = 16777215
%t A175824 Table[2^(8n) - 1, {n, 0, 11}]
%o A175824 (Python)
%o A175824 print([2**(8 * i) - 1 for i in range(12)])
%Y A175824 Cf. A000225. Equals A133752 minus one.
%K A175824 easy,nonn
%O A175824 0,2
%A A175824 _Grant Garcia_, Sep 13 2010