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

1,1

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).

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)

Example

a(1) = 2^7 - 1 = 128 - 1 = 127.
a(2) = 2^15 - 1 = 32768 - 1 = 32767.
a(3) = 2^23 - 1 = 8388608 - 1 = 8388607.

Mathematica

Table[2^(8n - 1) - 1, {n, 1, 11}]

Prog

(Python)
print([2**(8 * i - 1) - 1 for i in range(1, 12)])
(PARI) Vec(x*(127+128*x)/((1-x)*(1-256*x)) + O(x^50)) \\ Colin Barker, May 12 2016

Crossrefs

Cf. A000225, A175824.

Sequence in context: A289474 A069434 A175633 * A217914 A203798 A351134

Adjacent sequences: A175822 A175823 A175824 * A175826 A175827 A175828

Keyword

easy,less,nonn

Author

Grant Garcia, Sep 14 2010

Status

approved