A273153 a(n) = Numerator of (0 followed by 1's) - n/2^n.

0, 1, 1, 5, 3, 27, 29, 121, 31, 503, 507, 2037, 1021, 8179, 8185, 32753, 4095, 131055, 131063, 524269, 262139, 2097131, 2097141, 8388585, 2097149, 33554407, 33554419, 134217701, 67108857, 536870883, 536870897, 2147483617, 134217727, 8589934559, 8589934575, 34359738333

Offset: 0

Author

Paul Curtz, May 16 2016

Keywords

• nonn
• frac

Comments

A060576(n+1) = 0, 1, 1, 1, 1, 1, 1, ... - (0(n) = Oresme(n) = 0, 1/2, 1/2, 3/8, 1/4, 5/32, 3/32, ...). Both sequences are autosequences of the first kind. f(n) = 0, 1/2, 1/2, 5/8, 3/4, 27/32, 29/32, 121/128, ... is an autosequence of the first kind. Without one 1/2, f(n) is an increasing sequence.

The numerators (1 followed by A075101(n)) are the same as in n/2^n.

Examples

			Array of differences of fractions (characteristic aspect of an autosequence of the first kind):
0,     1/2,   1/2,   5/8,   3/4, ...
1/2,     0,   1/8,   1/8,  3/32, ...
-1/2,  1/8,     0, -1/32, -1/32, ...
5/8,  -1/8, -1/32,     0, 1/128, ...
-3/4, 3/32,  1/32, 1/128,     0, ...
...
		

Links

• OEIS Wiki, Autosequence

Crossrefs

Cf. A060576, A054977, A075101, A209308.

Programs

Mathematica

{0}~Join~Array[Numerator@ Abs[1 - Binomial[0, # - 1] - #/2^#] &, 30] (* Michael De Vlieger, May 17 2016 *)