A175825 Maximum signed integer that can be stored in n bytes.
127, 32767, 8388607, 2147483647, 549755813887, 140737488355327, 36028797018963967, 9223372036854775807, 2361183241434822606847, 604462909807314587353087, 154742504910672534362390527, 39614081257132168796771975167, 10141204801825835211973625643007
Offset: 1
Examples
a(1) = 2^7 - 1 = 128 - 1 = 127. a(2) = 2^15 - 1 = 32768 - 1 = 32767. a(3) = 2^23 - 1 = 8388608 - 1 = 8388607.
Links
- Colin Barker, Table of n, a(n) for n = 1..400
- Wikipedia, Byte
- Index entries for linear recurrences with constant coefficients, signature (257,-256).
Programs
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Mathematica
Table[2^(8n - 1) - 1, {n, 1, 11}] -
PARI
Vec(x*(127+128*x)/((1-x)*(1-256*x)) + O(x^50)) \\ Colin Barker, May 12 2016
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Python
print([2**(8 * i - 1) - 1 for i in range(1, 12)])
Formula
a(n) = 2^(8*n - 1) - 1.
From Colin Barker, May 12 2016: (Start)
a(n) = 257*a(n-1)-256*a(n-2) for n>2.
G.f.: x*(127+128*x) / ((1-x)*(1-256*x)).
(End)