

A108177


Integers of the form 2^(4n1) 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
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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 }
a(n) =  a(n1)  a(n2) + 16*a(n6) + 16*a(n7) + 16*a(n8) 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



KEYWORD

sign,easy


AUTHOR

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


EXTENSIONS



STATUS

approved



