A245599 Numbers m with A030101(m) XOR A030109(m) = m for the binary representation of m.

1, 11, 91, 731, 5851, 46811, 374491, 2995931, 23967451, 191739611, 1533916891, 12271335131, 98170681051, 785365448411, 6282923587291, 50263388698331, 402107109586651, 3216856876693211, 25734855013545691, 205878840108365531, 1647030720866924251, 13176245766935394011

Offset

1,2

Comments

Sequence consists of all numbers with binary representation 1(011)*.

Links

Colin Barker, Table of n, a(n) for n = 1..1001

Index entries for linear recurrences with constant coefficients, signature (9,-8).

Formula

a(n) = 1(011)^(n-1) in binary representation.

a(n) = (5*8^n - 12)/28. - Giovanni Resta, Apr 25 2020

From Colin Barker, Apr 25 2020: (Start)

G.f.: x*(1 + 2*x) / ((1 - x)*(1 - 8*x)).

a(n) = 9*a(n-1) - 8*a(n-2) for n>2.

(End)

Example

A030101(11) = 13,  A030109(11) = 6, and 13 XOR 6 = (1101)_2 XOR (0110)_2 = (1011)_2 = 11, so 11 is in the sequence.

Mathematica

a[n_] := (5*8^n - 12)/28; Array[a, 20] (* Giovanni Resta, Apr 25 2020 *)

Prog

(PARI) Vec(x*(1 + 2*x) / ((1 - x)*(1 - 8*x)) + O(x^20)) \\ Colin Barker, Apr 25 2020

Crossrefs

Cf. A007088, A030109, A030101.

Sequence in context: A016160 A005062 A125374 * A126532 A226868 A199678

Adjacent sequences: A245596 A245597 A245598 * A245600 A245601 A245602

Keyword

nonn,base,easy

Author

Reinhard Muehlfeld, Jul 27 2014

Extensions

More terms from Giovanni Resta, Apr 25 2020

Status

approved