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%I #16 May 10 2020 07:19:38
%S -1,0,1,7,8,9,15,16,17,127,128,129,255,256,257,2047,2048,2049,4095,
%T 4096,4097,32767,32768,32769,65535,65536,65537,524287,524288,524289,
%U 1048575,1048576,1048577,8388607,8388608,8388609,16777215,16777216,16777217,134217727,134217728,134217729,268435455
%N Integers of the form 2^(4n-1) or 2^(4n), n>0 and their immediate neighbors, together with -1, 0 and 1.
%C 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.
%H <a href="/index/Rec#order_08">Index entries for linear recurrences with constant coefficients</a>, signature (-1,-1,0,0,0,16,16,16).
%F Union of integers: -1, 0, 1, (2^((4n)-1)) +/- { 0, 1 }, (2^(4n)) +/- { 0, 1 }
%F From _Chai Wah Wu_, Dec 23 2019: (Start)
%F a(n) = - a(n-1) - a(n-2) + 16*a(n-6) + 16*a(n-7) + 16*a(n-8) for n > 10.
%F 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)
%t 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 *)
%K sign,easy
%O 0,4
%A Henrik Lundquist (sploinker(AT)sploink.dk), Jun 13 2005
%E Edited by _Robert G. Wilson v_, Jun 14 2005
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