cp's OEIS Frontend

A175825 Maximum signed integer that can be stored in n bytes.

%I A175825 #14 May 19 2021 16:04:57
%S A175825 127,32767,8388607,2147483647,549755813887,140737488355327,
%T A175825 36028797018963967,9223372036854775807,2361183241434822606847,
%U A175825 604462909807314587353087,154742504910672534362390527,39614081257132168796771975167,10141204801825835211973625643007
%N A175825 Maximum signed integer that can be stored in n bytes.
%H A175825 Colin Barker, <a href="/A175825/b175825.txt">Table of n, a(n) for n = 1..400</a>
%H A175825 Wikipedia, <a href="http://en.wikipedia.org/wiki/Byte">Byte</a>
%H A175825 <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (257,-256).
%F A175825 a(n) = 2^(8*n - 1) - 1.
%F A175825 From _Colin Barker_, May 12 2016: (Start)
%F A175825 a(n) = 257*a(n-1)-256*a(n-2) for n>2.
%F A175825 G.f.: x*(127+128*x) / ((1-x)*(1-256*x)).
%F A175825 (End)
%e A175825 a(1) = 2^7 - 1 = 128 - 1 = 127.
%e A175825 a(2) = 2^15 - 1 = 32768 - 1 = 32767.
%e A175825 a(3) = 2^23 - 1 = 8388608 - 1 = 8388607.
%t A175825 Table[2^(8n - 1) - 1, {n, 1, 11}]
%o A175825 (Python)
%o A175825 print([2**(8 * i - 1) - 1 for i in range(1, 12)])
%o A175825 (PARI) Vec(x*(127+128*x)/((1-x)*(1-256*x)) + O(x^50)) \\ _Colin Barker_, May 12 2016
%Y A175825 Cf. A000225, A175824.
%K A175825 easy,less,nonn
%O A175825 1,1
%A A175825 _Grant Garcia_, Sep 14 2010