A176303 a(n) = abs(2^n-127).
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
Offset: 0
Examples
a(2) = abs(2^2-127) = abs(4-127) = abs(-123) = 123. - _Indranil Ghosh_, Feb 20 2017
References
- R. K. Guy, Unsolved problems in number theory, Vol.1, 1994, Springer-Verlag,pages 42-43.
Links
- Indranil Ghosh, Table of n, a(n) for n = 0..1000
- Index entries for linear recurrences with constant coefficients, signature (3,-2).
Programs
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Mathematica
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 *) -
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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PARI
a(n)=abs(2^n-127) \\ Charles R Greathouse IV, Feb 20 2017
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Python
def A176303(n): return abs(2**n-127) # Indranil Ghosh, Feb 20 2017
Formula
From Colin Barker, Feb 20 2017: (Start)
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)
Comments