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A088163
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Numbers for which rotating one binary place to the right less rotating one binary place to the left is equal to zero.
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6
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0, 1, 2, 3, 7, 10, 15, 31, 42, 63, 127, 170, 255, 511, 682, 1023, 2047, 2730, 4095, 8191, 10922, 16383, 32767, 43690, 65535, 131071, 174762, 262143, 524287, 699050, 1048575, 2097151, 2796202, 4194303, 8388607, 11184810, 16777215, 33554431, 44739242, 67108863
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OFFSET
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0,3
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COMMENTS
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LINKS
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FORMULA
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a(n) = 5*a(n-3)-4*a(n-6) for n>5.
G.f.: x*(1+x)*(1+x+2*x^2) / ((1-x)*(1+x+x^2)*(1-4*x^3)).
(End)
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MATHEMATICA
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f[n_] := FromDigits[ RotateRight[ IntegerDigits[n, 2]], 2] - FromDigits[ RotateLeft[ IntegerDigits[n, 2]], 2]; Select[ Range[33560000], f[ # ] == 0 &]
(* Or *) Union[ Join[ Table[2^n - 1, {n, 0, 25}], Table[ Ceiling[2(2^n - 1)/3], {n, 2, 24, 2}]]]
LinearRecurrence[{0, 0, 5, 0, 0, -4}, {0, 1, 2, 3, 7, 10}, 40] (* Harvey P. Dale, Feb 20 2022 *)
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PROG
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(PARI) concat(0, Vec(x*(1+x)*(1+x+2*x^2) / ((1-x)*(1+x+x^2)*(1-4*x^3)) + O(x^50))) \\ Colin Barker, May 14 2016
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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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