A088163 Numbers for which rotating one binary place to the right less rotating one binary place to the left is equal to zero.

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

Offset

0,3

Comments

n is a member iff n is of the form 2^n -1 (A000225) or A000975(2n).

Links

Colin Barker, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (0,0,5,0,0,-4).

Formula

Numbers n such that A038572(n) - A006257(n) = A088161(n) = 0.

From Colin Barker, May 14 2016: (Start)

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)

Mathematica

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 *)

Prog

(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

Crossrefs

Cf. A000225, A000975.

Sequence in context: A370639 A361859 A192116 * A048448 A240302 A281611

Adjacent sequences: A088160 A088161 A088162 * A088164 A088165 A088166

Keyword

nonn,easy

Author

Robert G. Wilson v, Sep 13 2003

Status

approved