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A108177 Integers of the form 2^(4n-1) or 2^(4n), n>0 and their immediate neighbors, together with -1, 0 and 1. 0
-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 (list; graph; refs; listen; history; text; internal format)
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
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
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

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Last modified April 18 02:22 EDT 2024. Contains 371767 sequences. (Running on oeis4.)