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A176303
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a(n) = abs(2^n-127).
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5
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126, 125, 123, 119, 111, 95, 63, 1, 129, 385, 897, 1921, 3969, 8065, 16257, 32641, 65409, 130945, 262017, 524161, 1048449, 2097025, 4194177, 8388481, 16777089, 33554305, 67108737, 134217601, 268435329, 536870785, 1073741697, 2147483521, 4294967169
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OFFSET
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0,1
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REFERENCES
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R. K. Guy, Unsolved problems in number theory, Vol.1, 1994, Springer-Verlag,pages 42-43.
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LINKS
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FORMULA
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a(n) = 2^n - 127 for n>6.
a(n) = 3*a(n-1) - 2*a(n-2) for n>8.
G.f.: (126 - 253*x + 2*x^7 + 252*x^8) / ((1 - x)*(1 - 2*x)).
(End)
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EXAMPLE
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a(2) = abs(2^2-127) = abs(4-127) = abs(-123) = 123. - Indranil Ghosh, Feb 20 2017
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MATHEMATICA
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Table[Abs[2^n-127], {n, 0, 32}] (* or *) CoefficientList[Series[(126 - 253*x + 2*x^7 + 252*x^8) / ((1 - x)*(1 - 2*x)) , {x, 0, 30}], x] (* Indranil Ghosh, Feb 20 2017 *)
LinearRecurrence[{3, -2}, {126, 125, 123, 119, 111, 95, 63, 1, 129}, 40] (* Harvey P. Dale, Feb 11 2024 *)
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PROG
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(PARI) Vec((126 - 253*x + 2*x^7 + 252*x^8) / ((1 - x)*(1 - 2*x)) + O(x^40)) \\ Colin Barker, Feb 20 2017
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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STATUS
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approved
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