OFFSET
0,2
COMMENTS
All a(n) for n > 0 are Mersenne numbers. None are Mersenne primes.
LINKS
Wikipedia, Byte
Wikipedia, Mersenne prime
Index entries for linear recurrences with constant coefficients, signature (257, -256).
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]
EXAMPLE
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
MATHEMATICA
Table[2^(8n) - 1, {n, 0, 11}]
PROG
(Python)
print([2**(8 * i) - 1 for i in range(12)])
CROSSREFS
KEYWORD
easy,nonn
AUTHOR
Grant Garcia, Sep 13 2010
STATUS
approved