A108177 Integers of the form 2^(4n-1) or 2^(4n), n>0 and their immediate neighbors, together with -1, 0 and 1.

-1, 0, 1, 7, 8, 9, 15, 16, 17, 127, 128, 129, 255, 256, 257, 2047, 2048, 2049, 4095, 4096, 4097, 32767, 32768, 32769, 65535, 65536, 65537, 524287, 524288, 524289, 1048575, 1048576, 1048577, 8388607, 8388608, 8388609, 16777215, 16777216, 16777217, 134217727, 134217728, 134217729, 268435455

Offset

0,4

Comments

These integers are generated as a subset of interesting "areas" in typical microprocessor designs often based on 8, 16, 24, 32, 40, 56, 64 or 80 bits of precision and includes those areas where the sign representation could cause some design error. The numbers -1, 0, 1 represent a special case since they should and will be represented by a higher order number in the limited number space of N bits.

Links

Table of n, a(n) for n=0..42.

Index entries for linear recurrences with constant coefficients, signature (-1,-1,0,0,0,16,16,16).

Formula

Union of integers: -1, 0, 1, (2^((4n)-1)) +/- { 0, 1 }, (2^(4n)) +/- { 0, 1 }

From Chai Wah Wu, Dec 23 2019: (Start)

a(n) = - a(n-1) - a(n-2) + 16*a(n-6) + 16*a(n-7) + 16*a(n-8) for n > 10.

G.f.: (-16*x^10 - 32*x^9 - 48*x^8 - 56*x^7 - 48*x^6 - 24*x^5 - 16*x^4 - 8*x^3 + x + 1)/((4*x^3 - 1)*(4*x^3 + 1)*(x^2 + x + 1)). (End)

Mathematica

Join[{-1, 0, 1}, Sort[ Flatten[ NestList[{# - 1, # + 1} &, Flatten[ Table[{2^(4n - 1), 2^(4n)}, {n, 6}]], 1]]]] (* Robert G. Wilson v, Jun 14 2005 *)

Crossrefs

Sequence in context: A076599 A067197 A047523 * A165480 A285468 A060258

Adjacent sequences: A108174 A108175 A108176 * A108178 A108179 A108180

Keyword

sign,easy

Author

Henrik Lundquist (sploinker(AT)sploink.dk), Jun 13 2005

Extensions

Edited by Robert G. Wilson v, Jun 14 2005

Status

approved