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

0, 255, 65535, 16777215, 4294967295, 1099511627775, 281474976710655, 72057594037927935, 18446744073709551615, 4722366482869645213695, 1208925819614629174706175, 309485009821345068724781055

Offset: 0

Author

Grant Garcia, Sep 13 2010

Keywords

• easy
• nonn

Comments

All a(n) for n > 0 are Mersenne numbers. None are Mersenne primes.

Examples

			a(0) = 2^0 - 1 = 1 - 1 = 0
a(1) = 2^8 - 1 = 256 - 1 = 255
a(2) = 2^16 - 1 = 65536 - 1 = 65535
a(3) = 2^24 - 1 = 16777216 - 1 = 16777215
		

Links

• Wikipedia, Byte
• Wikipedia, Mersenne prime
• Index entries for linear recurrences with constant coefficients, signature (257, -256).

Crossrefs

Cf. A000225. Equals A133752 minus one.

Programs

Mathematica

Table[2^(8n) - 1, {n, 0, 11}]

Python

print([2**(8 * i) - 1 for i in range(12)])

Formula

a(n) = 2^(8*n) - 1.

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]